Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm
Purpose The purpose of this study is to introduce the reproducing kernel algorithm for treating classes of time-fractional partial differential equations subject to Robin boundary conditions with parameters derivative arising in fluid flows, fluid dynamics, groundwater hydrology, conservation of ene...
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| Vydané v: | International journal of numerical methods for heat & fluid flow Ročník 28; číslo 4; s. 828 - 856 |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Bradford
Emerald Publishing Limited
03.04.2018
Emerald Group Publishing Limited |
| Predmet: | |
| ISSN: | 0961-5539, 1758-6585 |
| On-line prístup: | Získať plný text |
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| Abstract | Purpose
The purpose of this study is to introduce the reproducing kernel algorithm for treating classes of time-fractional partial differential equations subject to Robin boundary conditions with parameters derivative arising in fluid flows, fluid dynamics, groundwater hydrology, conservation of energy, heat conduction and electric circuit.
Design/methodology/approach
The method provides appropriate representation of the solutions in convergent series formula with accurately computable components. This representation is given in the W(Ω) and H(Ω) inner product spaces, while the computation of the required grid points relies on the R(y,s) (x, t) and r(y,s) (x, t) reproducing kernel functions.
Findings
Numerical simulation with different order derivatives degree is done including linear and nonlinear terms that are acquired by interrupting the n-term of the exact solutions. Computational results showed that the proposed algorithm is competitive in terms of the quality of the solutions found and is very valid for solving such time-fractional models.
Research limitations/implications
Future work includes the application of the reproducing kernel algorithm to highly nonlinear time-fractional partial differential equations such as those arising in single and multiphase flows. The results will be published in forthcoming papers.
Practical implications
The study included a description of fundamental reproducing kernel algorithm and the concepts of convergence, and error behavior for the reproducing kernel algorithm solvers. Results obtained by the proposed algorithm are found to outperform in terms of accuracy, generality and applicability.
Social implications
Developing analytical and numerical methods for the solutions of time-fractional partial differential equations is a very important task owing to their practical interest.
Originality/value
This study, for the first time, presents reproducing kernel algorithm for obtaining the numerical solutions of some certain classes of Robin time-fractional partial differential equations. An efficient construction is provided to obtain the numerical solutions for the equations, along with an existence proof of the exact solutions based upon the reproducing kernel theory. |
|---|---|
| AbstractList | Purpose
The purpose of this study is to introduce the reproducing kernel algorithm for treating classes of time-fractional partial differential equations subject to Robin boundary conditions with parameters derivative arising in fluid flows, fluid dynamics, groundwater hydrology, conservation of energy, heat conduction and electric circuit.
Design/methodology/approach
The method provides appropriate representation of the solutions in convergent series formula with accurately computable components. This representation is given in the W(Ω) and H(Ω) inner product spaces, while the computation of the required grid points relies on the R(y,s) (x, t) and r(y,s) (x, t) reproducing kernel functions.
Findings
Numerical simulation with different order derivatives degree is done including linear and nonlinear terms that are acquired by interrupting the n-term of the exact solutions. Computational results showed that the proposed algorithm is competitive in terms of the quality of the solutions found and is very valid for solving such time-fractional models.
Research limitations/implications
Future work includes the application of the reproducing kernel algorithm to highly nonlinear time-fractional partial differential equations such as those arising in single and multiphase flows. The results will be published in forthcoming papers.
Practical implications
The study included a description of fundamental reproducing kernel algorithm and the concepts of convergence, and error behavior for the reproducing kernel algorithm solvers. Results obtained by the proposed algorithm are found to outperform in terms of accuracy, generality and applicability.
Social implications
Developing analytical and numerical methods for the solutions of time-fractional partial differential equations is a very important task owing to their practical interest.
Originality/value
This study, for the first time, presents reproducing kernel algorithm for obtaining the numerical solutions of some certain classes of Robin time-fractional partial differential equations. An efficient construction is provided to obtain the numerical solutions for the equations, along with an existence proof of the exact solutions based upon the reproducing kernel theory. PurposeThe purpose of this study is to introduce the reproducing kernel algorithm for treating classes of time-fractional partial differential equations subject to Robin boundary conditions with parameters derivative arising in fluid flows, fluid dynamics, groundwater hydrology, conservation of energy, heat conduction and electric circuit.Design/methodology/approachThe method provides appropriate representation of the solutions in convergent series formula with accurately computable components. This representation is given in the W(Ω) and H(Ω) inner product spaces, while the computation of the required grid points relies on the R(y,s) (x, t) and r(y,s) (x, t) reproducing kernel functions.FindingsNumerical simulation with different order derivatives degree is done including linear and nonlinear terms that are acquired by interrupting the n-term of the exact solutions. Computational results showed that the proposed algorithm is competitive in terms of the quality of the solutions found and is very valid for solving such time-fractional models.Research limitations/implicationsFuture work includes the application of the reproducing kernel algorithm to highly nonlinear time-fractional partial differential equations such as those arising in single and multiphase flows. The results will be published in forthcoming papers.Practical implicationsThe study included a description of fundamental reproducing kernel algorithm and the concepts of convergence, and error behavior for the reproducing kernel algorithm solvers. Results obtained by the proposed algorithm are found to outperform in terms of accuracy, generality and applicability.Social implicationsDeveloping analytical and numerical methods for the solutions of time-fractional partial differential equations is a very important task owing to their practical interest.Originality/valueThis study, for the first time, presents reproducing kernel algorithm for obtaining the numerical solutions of some certain classes of Robin time-fractional partial differential equations. An efficient construction is provided to obtain the numerical solutions for the equations, along with an existence proof of the exact solutions based upon the reproducing kernel theory. |
| Author | Abu Arqub, Omar |
| Author_xml | – sequence: 1 givenname: Omar surname: Abu Arqub fullname: Abu Arqub, Omar email: o.abuarqub@bau.edu.jo |
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| Cites_doi | 10.1080/10407790.2013.778719 10.1080/10618560903367759 10.1016/j.jcp.2014.08.004 10.1016/S0165-1684(03)00181-6 10.1016/j.matcom.2016.08.002 10.1002/fld.3936 10.1016/j.camwa.2016.02.024 10.1007/s00521-015-2110-x 10.18576/amis/100429 10.1063/1.4825908 10.1007/s00521-016-2484-4 10.1016/j.aml.2013.05.006 10.1504/IJCSM.2013.054668 10.1007/s10910-014-0384-3 10.1615/InterJFluidMechRes.v41.i6.70 10.1016/j.cnsns.2010.12.019 10.1007/s00500-015-1707-4 10.1002/mma.3884 10.1016/j.cpc.2014.03.025 10.1016/j.amc.2012.12.009 10.1002/num.21947 10.1016/j.camwa.2015.04.030 10.1016/j.amc.2013.03.123 10.1016/j.amc.2013.03.006 10.1016/j.cam.2013.04.040 10.1016/j.amc.2005.11.025 10.1016/j.camwa.2016.01.001 10.1016/j.chaos.2005.09.002 10.1016/j.amc.2014.06.063 10.1002/num.22046 10.1108/09615531211199818 10.1016/j.jcp.2014.09.034 10.1088/0031-8949/75/1/008 10.1016/j.apm.2015.01.021 10.1016/j.amc.2007.05.048 10.1002/mma.4023 10.1016/j.aml.2005.10.010 10.1016/j.cam.2009.01.012 10.1007/s00500-016-2262-3 10.1016/j.cam.2015.11.037 10.1515/fca-2015-0045 10.1016/j.amc.2014.12.121 10.1155/2015/457013 |
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| Keywords | Heat Gas dynamics Reproducing kernel algorithm Time-fractional partial differential equations Navier–Stokes Burgers’ and Fitzhugh–Nagumo equations Robin boundary conditions Advection–diffusion |
| Language | English |
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| References | (key2024092312243986000_ref005) 2014; 243 (key2024092312243986000_ref047) 2008; 196 (key2024092312243986000_ref025) 2011; 16 (key2024092312243986000_ref021) 2015 (key2024092312243986000_ref054) 2009; 23 (key2024092312243986000_ref040) 2017; 132 (key2024092312243986000_ref006) 2013; 219 (key2024092312243986000_ref031) 2006; 19 (key2024092312243986000_ref052) 2015; 70 (key2024092312243986000_ref014) 2003 (key2024092312243986000_ref002) 2016; 39 (key2024092312243986000_ref032) 2006; 28 (key2024092312243986000_ref055) 2014; 76 (key2024092312243986000_ref013) 2009 (key2024092312243986000_ref028) 2006 (key2024092312243986000_ref001) 2015; 28 (key2024092312243986000_ref004) 2016; 145 (key2024092312243986000_ref019) 2015; 39 (key2024092312243986000_ref008) 2015; 20 (key2024092312243986000_ref039) 2015; 39 (key2024092312243986000_ref010) 2004 (key2024092312243986000_ref018) 2013; 26 (key2024092312243986000_ref024) 2013; 219 (key2024092312243986000_ref044) 2014; 52 (key2024092312243986000_ref046) 2016; 11 (key2024092312243986000_ref048) 2015; 2015 (key2024092312243986000_ref053) 2008 (key2024092312243986000_ref011) 2015; 18 (key2024092312243986000_ref051) 1982 (key2024092312243986000_ref022) 2000 (key2024092312243986000_ref020) 2014; 255 (key2024092312243986000_ref003) 2016; 29 (key2024092312243986000_ref012) 2016; 71 (key2024092312243986000_ref057) 2015; 31 (key2024092312243986000_ref023) 2016; 32 (key2024092312243986000_ref038) 2013; 63 (key2024092312243986000_ref036) 2003; 83 (key2024092312243986000_ref007) 2015; 293 (key2024092312243986000_ref037) 2013 (key2024092312243986000_ref042) 2013; 4 (key2024092312243986000_ref017) 2015; 257 (key2024092312243986000_ref045) 2016; 10 (key2024092312243986000_ref015) 2008 (key2024092312243986000_ref034) 2017 (key2024092312243986000_ref058) 2009; 230 (key2024092312243986000_ref027) 2009; 10 (key2024092312243986000_ref035) 2006 (key2024092312243986000_ref029) 2014; 185 (key2024092312243986000_ref041) 2007; 75 (key2024092312243986000_ref050) 2013; 219 (key2024092312243986000_ref016) 2015; 293 (key2024092312243986000_ref030) 2016; 299 (key2024092312243986000_ref026) 2012; 22 (key2024092312243986000_ref056) 2014; 41 (key2024092312243986000_ref049) 2013; 14 (key2024092312243986000_ref009) 2016; 21 (key2024092312243986000_ref043) 2016; 71 (key2024092312243986000_ref033) 2006; 177 |
| References_xml | – volume: 63 start-page: 540 issue: 6 year: 2013 ident: key2024092312243986000_ref038 article-title: Higher-order numerical scheme for the fractional heat equation with Dirichlet and Neumann boundary conditions publication-title: Numerical Heat Transfer, Part B doi: 10.1080/10407790.2013.778719 – volume: 23 start-page: 623 issue: 9 year: 2009 ident: key2024092312243986000_ref054 article-title: Validation of hyperbolic model for two-phase flow in conservative form publication-title: International Journal of Computational Fluid Dynamics doi: 10.1080/10618560903367759 – volume: 39 start-page: 3075 issue: 10/11 year: 2015 ident: key2024092312243986000_ref039 article-title: An efficient computational intelligence approach for solving fractional order Riccati equations using ANN and SQP publication-title: Applied Mathematical Modeling – volume: 293 start-page: 81 year: 2015 ident: key2024092312243986000_ref016 article-title: Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: a new iterative algorithm publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2014.08.004 – volume: 83 start-page: 2285 issue: 11 year: 2003 ident: key2024092312243986000_ref036 article-title: Fractional signal processing and applications publication-title: Signal Process doi: 10.1016/S0165-1684(03)00181-6 – volume: 132 start-page: 139 year: 2017 ident: key2024092312243986000_ref040 article-title: Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley-Torvik equation publication-title: Computer and Mathematics in Simulations doi: 10.1016/j.matcom.2016.08.002 – volume: 76 start-page: 312 issue: 5 year: 2014 ident: key2024092312243986000_ref055 article-title: Application of a thermodynamically compatible two-phase flow model to the high-resolution simulations of compressible gas-magma flow publication-title: International Journal for Numerical Methods in Fluids doi: 10.1002/fld.3936 – volume: 71 start-page: 1818 issue: 9 year: 2016 ident: key2024092312243986000_ref012 article-title: Spectral methods for the time fractional diffusion–wave equation in a semi-infinite channel publication-title: Computers & Mathematics with Applications doi: 10.1016/j.camwa.2016.02.024 – volume: 28 start-page: 1591 issue: 7 year: 2015 ident: key2024092312243986000_ref001 article-title: Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations publication-title: Neural Computing & Applications doi: 10.1007/s00521-015-2110-x – volume-title: Reproducing Kernel Hilbert Space in Probability and Statistics year: 2004 ident: key2024092312243986000_ref010 – volume-title: Functional Fractional Calculus for System Identification and Controls year: 2008 ident: key2024092312243986000_ref015 – volume: 10 start-page: 1513 issue: 4 year: 2016 ident: key2024092312243986000_ref045 article-title: Application of novel schemes based on Haar wavelet collocation method for Burger and Boussinesq-Burger equations publication-title: Applied Mathematics & Information Sciences doi: 10.18576/amis/100429 – year: 2013 ident: key2024092312243986000_ref037 article-title: Exact solutions of the time-fractional Fitzhugh-Nagumo equation doi: 10.1063/1.4825908 – volume: 29 start-page: 1465 issue: 5 year: 2016 ident: key2024092312243986000_ref003 article-title: Maayah, solutions of Bagley-Torvik and Painlevé equations of fractional order using iterative reproducing kernel algorithm publication-title: Neural Computing & Applications doi: 10.1007/s00521-016-2484-4 – volume: 26 start-page: 998 issue: 10 year: 2013 ident: key2024092312243986000_ref018 article-title: Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers publication-title: Applied Mathematics Letters doi: 10.1016/j.aml.2013.05.006 – volume-title: Reproducing Kernel Hilbert Spaces: Applications in Statistical Signal Processing year: 1982 ident: key2024092312243986000_ref051 – volume: 4 start-page: 1 issue: 1 year: 2013 ident: key2024092312243986000_ref042 article-title: Numerical solutions of (1 + 1) dimensional time fractional coupled Burger equations using new coupled fractional reduced differential transform method publication-title: International Journal of Computing Science and Mathematics doi: 10.1504/IJCSM.2013.054668 – volume: 52 start-page: 2277 issue: 8 year: 2014 ident: key2024092312243986000_ref044 article-title: A two-dimensional Haar wavelet approach for the numerical simulations of time and space fractional Fokker-Planck equations in modelling of anomalous diffusion systems publication-title: Journal of Mathematical Chemistry doi: 10.1007/s10910-014-0384-3 – volume: 41 start-page: 547 issue: 6 year: 2014 ident: key2024092312243986000_ref056 article-title: Implementation of velocity and pressure non-equilibrium in gas-liquid two-phase flow computations publication-title: International Journal of Fluid Mechanics Research doi: 10.1615/InterJFluidMechRes.v41.i6.70 – volume: 16 start-page: 3639 issue: 9 year: 2011 ident: key2024092312243986000_ref025 article-title: Representation of exact solution for the time-fractional telegraph equation in the reproducing kernel space publication-title: Communications in Nonlinear Science and Numerical Simulation doi: 10.1016/j.cnsns.2010.12.019 – volume: 20 start-page: 3283 issue: 8 year: 2015 ident: key2024092312243986000_ref008 article-title: Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method publication-title: Soft Computing doi: 10.1007/s00500-015-1707-4 – volume: 39 start-page: 4549 issue: 15 year: 2016 ident: key2024092312243986000_ref002 article-title: The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations publication-title: Mathematical Methods in the Applied Sciences doi: 10.1002/mma.3884 – volume: 185 start-page: 1947 year: 2014 ident: key2024092312243986000_ref029 article-title: New analytical method for gas dynamics equation arising in shock fronts publication-title: Computer Physics Communications doi: 10.1016/j.cpc.2014.03.025 – volume: 219 start-page: 5918 issue: 11 year: 2013 ident: key2024092312243986000_ref050 article-title: Using reproducing kernel for solving a class of fractional partial differential equation with non-classical conditions publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2012.12.009 – volume: 31 start-page: 1345 issue: 5 year: 2015 ident: key2024092312243986000_ref057 article-title: A series of high-order quasi-compact schemes for space fractional diffusion equations based on the superconvergent approximations for fractional derivatives publication-title: Numerical Methods for Partial Differential Equations doi: 10.1002/num.21947 – volume: 70 start-page: 254 year: 2015 ident: key2024092312243986000_ref052 article-title: The method of approximate particular solutions for the time-fractional diffusion equation with a non-local boundary condition publication-title: Computers & Mathematics with Applications doi: 10.1016/j.camwa.2015.04.030 – volume: 219 start-page: 10225 issue: 20 year: 2013 ident: key2024092312243986000_ref024 article-title: Solving a system of linear Volterra integral equations using the new reproducing kernel method publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2013.03.123 – volume: 145 start-page: 1 year: 2016 ident: key2024092312243986000_ref004 article-title: Approximate solutions of DASs with nonclassical boundary conditions using novel reproducing kernel algorithm publication-title: Fundamenta Informaticae – volume: 219 start-page: 8938 issue: 17 year: 2013 ident: key2024092312243986000_ref006 article-title: Solving Fredholm integro-differential equations using reproducing kernel hilbert space method publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2013.03.006 – volume: 255 start-page: 97 year: 2014 ident: key2024092312243986000_ref020 article-title: A numerical method for singularly perturbed turning point problems with an interior layer publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2013.04.040 – volume-title: The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order year: 2006 ident: key2024092312243986000_ref035 – volume: 177 start-page: 488 issue: 2 year: 2006 ident: key2024092312243986000_ref033 article-title: Analytical solution of a time-fractional Navier-stokes equation by Adomian decomposition method publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2005.11.025 – volume-title: Applications of Fractional Calculus in Physics year: 2000 ident: key2024092312243986000_ref022 – volume: 71 start-page: 859 year: 2016 ident: key2024092312243986000_ref043 article-title: New exact solutions of nonlinear fractional acoustic wave equations in ultrasound publication-title: Computers & Mathematics with Applications doi: 10.1016/j.camwa.2016.01.001 – volume: 28 start-page: 930 issue: 4 year: 2006 ident: key2024092312243986000_ref032 article-title: Non-perturbative analytical solutions of the space- and time-fractional burgers equations publication-title: Chaos, Solitons & Fractals doi: 10.1016/j.chaos.2005.09.002 – volume: 243 start-page: 911 year: 2014 ident: key2024092312243986000_ref005 article-title: Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2014.06.063 – volume: 32 start-page: 1184 issue: 4 year: 2016 ident: key2024092312243986000_ref023 article-title: High-order compact finite difference and Laplace transform method for the solution of time-fractional heat equations with Dirchlet and Neumann boundary conditions publication-title: Numerical Methods for Partial Differential Equations doi: 10.1002/num.22046 – volume: 22 start-page: 175 year: 2012 ident: key2024092312243986000_ref026 article-title: Numerical solutions of time-fractional Burgers equations: a comparison between generalized differential transformation technique and homotopy perturbation method publication-title: International Journal of Numerical Methods for Heat & Fluid Flow doi: 10.1108/09615531211199818 – volume: 293 start-page: 385 year: 2015 ident: key2024092312243986000_ref007 article-title: Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2014.09.034 – volume-title: Fractional Partial Differential Equations and Their Numerical Solutions year: 2015 ident: key2024092312243986000_ref021 – volume: 75 start-page: 53 issue: 1 year: 2007 ident: key2024092312243986000_ref041 article-title: Exact solutions for time-fractional diffusion-wave equations by decomposition method publication-title: Physica Scripta doi: 10.1088/0031-8949/75/1/008 – volume: 39 start-page: 5592 issue: 18 year: 2015 ident: key2024092312243986000_ref019 article-title: Modified reproducing kernel method for singularly perturbed boundary value problems with a delay publication-title: Applied Mathematical Modelling doi: 10.1016/j.apm.2015.01.021 – volume: 196 start-page: 294 issue: 1 year: 2008 ident: key2024092312243986000_ref047 article-title: Application of modified decomposition method for the analytical solution of space fractional diffusion equation publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2007.05.048 – year: 2017 ident: key2024092312243986000_ref034 article-title: Modified iteration method for solving fractional gas dynamics equation publication-title: Mathematical Methods in the Applied Sciences doi: 10.1002/mma.4023 – volume-title: Theory and Applications of Fractional Differential Equations year: 2006 ident: key2024092312243986000_ref028 – volume: 19 start-page: 808 issue: 8 year: 2006 ident: key2024092312243986000_ref031 article-title: Representation of the exact solution for a kind of nonlinear partial differential equations publication-title: Applied Mathematics Letters doi: 10.1016/j.aml.2005.10.010 – volume-title: Nonlinear Numerical Analysis in the Reproducing Kernel Space year: 2009 ident: key2024092312243986000_ref013 – volume: 230 start-page: 770 issue: 2 year: 2009 ident: key2024092312243986000_ref058 article-title: Numerical algorithm for parabolic problems with non-classical conditions publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2009.01.012 – volume: 21 start-page: 7191 issue: 23 year: 2016 ident: key2024092312243986000_ref009 article-title: Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems publication-title: Soft Computing doi: 10.1007/s00500-016-2262-3 – volume: 14 start-page: 875 issue: 1 year: 2013 ident: key2024092312243986000_ref049 article-title: Inverse heat problem of determining time-dependent source parameter in reproducing kernel space publication-title: Nonlinear Analysis: Real World Applications – volume: 299 start-page: 159 year: 2016 ident: key2024092312243986000_ref030 article-title: High-order approximation to Caputo derivatives and Caputo-type advection–diffusion equations (III) publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2015.11.037 – volume: 11 start-page: 1 year: 2016 ident: key2024092312243986000_ref046 article-title: Numerical solution of fractional partial differential equation of parabolic type with Dirichlet boundary conditions using two-dimensional Legendre wavelets method publication-title: Journal of Computational and Nonlinear Dynamics – start-page: 1 year: 2008 ident: key2024092312243986000_ref053 article-title: Reproducing kernel methods for solving linear initial-boundary-value problems publication-title: Electronic Journal of Differential Equations – volume: 18 start-page: 735 year: 2015 ident: key2024092312243986000_ref011 article-title: High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II) publication-title: Fractional Calculus and Applied Analysis doi: 10.1515/fca-2015-0045 – volume-title: Reproducing Kernel Spaces and Applications year: 2003 ident: key2024092312243986000_ref014 – volume: 257 start-page: 119 year: 2015 ident: key2024092312243986000_ref017 article-title: A novel expansion iterative method for solving linear partial differential equations of fractional order publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2014.12.121 – volume: 10 start-page: 1127 year: 2009 ident: key2024092312243986000_ref027 article-title: Analytical study of NAVIER-stokes equation with fractional orders using He’s homotopy perturbation and variational iteration methods publication-title: International Journal of Nonlinear Sciences and Numerical Simulation – volume: 2015 start-page: 13 year: 2015 ident: key2024092312243986000_ref048 article-title: A new approach and solution technique to solve time fractional nonlinear reaction-diffusion equations publication-title: Mathematical Problems in Engineering doi: 10.1155/2015/457013 |
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| SubjectTerms | Algorithms Applied mathematics Boundary conditions Circuit design Circuits Computation Computational fluid dynamics Computer simulation Conduction heating Conductive heat transfer Convergence Differential equations Differential thermal analysis Dynamics Energy conservation Engineering Exact solutions Fluid dynamics Fluid flow Groundwater Groundwater treatment Heat conduction Heat transfer Hilbert space Hydrodynamics Hydrologic models Hydrology Kernel functions Mathematical analysis Mathematical functions Mathematical models Multiphase flow Nonlinear equations Numerical methods Numerical models Partial differential equations Physics Realism Representations Series (mathematics) Solutions Solvers |
| Title | Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm |
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