Reproducing Kernel Algorithm for the Analytical-Numerical Solutions of Nonlinear Systems of Singular Periodic Boundary Value Problems

The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order periodic boundary value problems with finitely many singularities. The analytical-numerical solutions are obtained in the form of an infinite...

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Vydáno v:Mathematical problems in engineering Ročník 2015; číslo 2015; s. 1 - 13
Hlavní autor: Abu Arqub, Omar
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cairo, Egypt Hindawi Publishing Corporation 01.01.2015
John Wiley & Sons, Inc
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ISSN:1024-123X, 1563-5147
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Abstract The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order periodic boundary value problems with finitely many singularities. The analytical-numerical solutions are obtained in the form of an infinite convergent series for appropriate periodic boundary conditions in the space W230,1, whilst two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach. The main characteristic feature of the utilized algorithm is that the global approximation can be established on the whole solution domain, in contrast with other numerical methods like onestep and multistep methods, and the convergence is uniform. Two numerical experiments are carried out to verify the mathematical results, whereas the theoretical statements for the solutions are supported by the results of numerical experiments. Our results reveal that the present algorithm is a very effective and straightforward way of formulating the analytical-numerical solutions for such nonlinear periodic singular systems.
AbstractList The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order periodic boundary value problems with finitely many singularities. The analytical-numerical solutions are obtained in the form of an infinite convergent series for appropriate periodic boundary conditions in the space W230,1, whilst two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach. The main characteristic feature of the utilized algorithm is that the global approximation can be established on the whole solution domain, in contrast with other numerical methods like onestep and multistep methods, and the convergence is uniform. Two numerical experiments are carried out to verify the mathematical results, whereas the theoretical statements for the solutions are supported by the results of numerical experiments. Our results reveal that the present algorithm is a very effective and straightforward way of formulating the analytical-numerical solutions for such nonlinear periodic singular systems.
The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order periodic boundary value problems with finitely many singularities. The analytical-numerical solutions are obtained in the form of an infinite convergent series for appropriate periodic boundary conditions in the space [superscript]W23[/superscript] [0,1], whilst two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach. The main characteristic feature of the utilized algorithm is that the global approximation can be established on the whole solution domain, in contrast with other numerical methods like onestep and multistep methods, and the convergence is uniform. Two numerical experiments are carried out to verify the mathematical results, whereas the theoretical statements for the solutions are supported by the results of numerical experiments. Our results reveal that the present algorithm is a very effective and straightforward way of formulating the analytical-numerical solutions for such nonlinear periodic singular systems.
The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order periodic boundary value problems with finitely many singularities. The analytical-numerical solutions are obtained in the form of an infinite convergent series for appropriate periodic boundary conditions in the space super(W23) 0,1, whilst two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach. The main characteristic feature of the utilized algorithm is that the global approximation can be established on the whole solution domain, in contrast with other numerical methods like onestep and multistep methods, and the convergence is uniform. Two numerical experiments are carried out to verify the mathematical results, whereas the theoretical statements for the solutions are supported by the results of numerical experiments. Our results reveal that the present algorithm is a very effective and straightforward way of formulating the analytical-numerical solutions for such nonlinear periodic singular systems.
The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order periodic boundary value problems with finitely many singularities. The analytical-numerical solutions are obtained in the form of an infinite convergent series for appropriate periodic boundary conditions in the space W 2 3 0,1 , whilst two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach. The main characteristic feature of the utilized algorithm is that the global approximation can be established on the whole solution domain, in contrast with other numerical methods like onestep and multistep methods, and the convergence is uniform. Two numerical experiments are carried out to verify the mathematical results, whereas the theoretical statements for the solutions are supported by the results of numerical experiments. Our results reveal that the present algorithm is a very effective and straightforward way of formulating the analytical-numerical solutions for such nonlinear periodic singular systems.
Author Abu Arqub, Omar
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Cites_doi 10.1016/j.amc.2014.06.063
10.1007/978-1-4419-9096-9
10.1016/j.apnum.2005.04.012
10.1155/2012/205391
10.1155/2014/135465
10.1155/2012/839836
10.1016/j.cam.2013.04.040
10.1007/s10915-007-9141-0
10.1016/j.aml.2005.10.010
10.1016/j.jmaa.2006.10.006
10.1007/978-3-0348-8077-0
10.1006/jcph.1999.6262
10.1017/S0022143000016233
10.1016/j.amc.2010.01.038
10.1002/num.21809
10.1016/j.amc.2013.03.123
10.1155/2013/832074
10.1016/j.amc.2007.03.016
10.1016/j.aml.2013.05.006
10.1016/s0096-3003(02)00370-3
10.1155/2014/758195
10.1016/s0096-3003(02)00919-0
10.1137/1.9781611971231
10.1016/j.amc.2013.03.006
10.1016/j.jmaa.2006.06.053
10.1016/j.amc.2008.12.019
10.1016/j.amc.2014.04.057
10.1016/j.jmaa.2006.06.054
10.1016/j.camwa.2006.07.014
10.12785/amis/080617
10.1016/j.aml.2011.10.025
ContentType Journal Article
Copyright Copyright © 2015 Omar Abu Arqub.
Copyright © 2015 Omar Abu Arqub. Omar Abu Arqub et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright_xml – notice: Copyright © 2015 Omar Abu Arqub.
– notice: Copyright © 2015 Omar Abu Arqub. Omar Abu Arqub et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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References (6) 2004; 148
(30) 2014; 2014
(14) 2007; 328
(21) 2008; 2008
Lima P. Chemetov N. Konyukhova N. Sukov A. Analytical-numerical approach to a singular boundary value problem Proceedings of 24th CILAMCE Ouro Preto, Brazil
(9) 2012; 2012
(25) 2012; 2012
(32) 2007; 192
(36) 2013; 26
(27) 2014; 16
(34) 2013; 219
(38) 2014; 255
Daniel A. Reproducing Kernel Spaces and Applications 2003 Basel, Switzerland Springer 10.1007/978-3-0348-8077-0 MR2019345
(3) 2007; 32
(1) 1999; 152
(5) 2007; 332
(22) 2014; 243
(12) 2009; 208
31
(11) 2010; 216
(15) 2007; 53
(33) 2003; 143
Cui M. Lin Y. Nonlinear Numerical Analysis in the Reproducing Kernel Space 2009 New York, NY, USA Nova Science MR2502102
(29) 2015; 8
(10) 2014; 8
Berlinet A. Thomas-Agnan C. Reproducing Kernel Hilbert Spaces in Probability and Statistics 2004 Boston, Mass, USA Kluwer Academic Publishers 10.1007/978-1-4419-9096-9 MR2239907
(2) 2006; 56
(23) 2014; 240
(24) 2013; 2013
(28) 2014; 2014
(37) 2014; 30
(20) 2006; 19
(35) 2012; 25
(7) 1995; 41
(26) 2013; 219
(13) 2007; 329
Ascher U. M. Mattheij R. M. Russell R. D. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations 1995 13 Philadelphia, Pa, USA SIAM Classics in Applied Mathematics 10.1137/1.9781611971231 MR1351005
Weinert H. L. Reproducing Kernel Hilbert Spaces: Applications in Statistical Signal Processing 1982 Hutchinson Ross
22
23
24
25
26
28
(16) 2009
(19) 1982
30
10
32
11
33
12
34
13
35
14
36
15
37
38
17
18
1
2
3
5
6
8
9
20
References_xml – ident: 31
  article-title: Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method
– volume: 240
  start-page: 229
  year: 2014
  end-page: 239
  ident: 23
  article-title: A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm-Volterra type
– reference: Lima P. Chemetov N. Konyukhova N. Sukov A. Analytical-numerical approach to a singular boundary value problem Proceedings of 24th CILAMCE Ouro Preto, Brazil
– volume: 8
  start-page: 857
  year: 2015
  end-page: 874
  ident: 29
  article-title: An iterative method for solving fourth-order boundary value problems of mixed type integro-differential equations
– volume: 152
  start-page: 756
  issue: 2
  year: 1999
  end-page: 789
  ident: 1
  article-title: New self-similar solutions of the nonlinear Schrödinger equation with moving mesh computations
– volume: 328
  start-page: 1255
  issue: 2
  year: 2007
  end-page: 1267
  ident: 14
  article-title: Positive solution of singular Dirichlet boundary value problems for second order differential equation system
– volume: 2013
  year: 2013
  end-page: 10
  ident: 24
  article-title: A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations
– reference: Weinert H. L. Reproducing Kernel Hilbert Spaces: Applications in Statistical Signal Processing 1982 Hutchinson Ross
– volume: 2008
  issue: 29
  year: 2008
  end-page: 11
  ident: 21
  article-title: Reproducing kernel methods for solving linear initial-boundary-value problems
– volume: 56
  start-page: 413
  issue: 3-4
  year: 2006
  end-page: 422
  ident: 2
  article-title: From nonlinear PDEs to singular ODEs
– volume: 2014
  year: 2014
  end-page: 7
  ident: 30
  article-title: Iterative multistep reproducing kernel Hilbert space method for solving strongly nonlinear oscillators
– volume: 208
  start-page: 511
  issue: 2
  year: 2009
  end-page: 519
  ident: 12
  article-title: Positive solutions of a singular boundary value problem for systems of second-order differential equations
– reference: Ascher U. M. Mattheij R. M. Russell R. D. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations 1995 13 Philadelphia, Pa, USA SIAM Classics in Applied Mathematics 10.1137/1.9781611971231 MR1351005
– volume: 332
  start-page: 523
  issue: 1
  year: 2007
  end-page: 541
  ident: 5
  article-title: On a singular boundary value problem arising in the theory of shallow membrane caps
– volume: 192
  start-page: 389
  issue: 2
  year: 2007
  end-page: 398
  ident: 32
  article-title: Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space
– volume: 219
  start-page: 10225
  issue: 20
  year: 2013
  end-page: 10230
  ident: 34
  article-title: Solving a system of linear Volterra integral equations using the new reproducing kernel method
– volume: 329
  start-page: 851
  issue: 2
  year: 2007
  end-page: 869
  ident: 13
  article-title: Fixed-sign solutions for a system of singular focal boundary value problems
– volume: 143
  start-page: 393
  issue: 2-3
  year: 2003
  end-page: 399
  ident: 33
  article-title: The exact solution for solving a class nonlinear operator equations in the reproducing kernel space
– volume: 243
  start-page: 911
  year: 2014
  end-page: 922
  ident: 22
  article-title: Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations
– volume: 16
  start-page: 750
  issue: 4
  year: 2014
  end-page: 762
  ident: 27
  article-title: Analytical solution of nonlinear second-order periodic boundary value problem using reproducing kernel method
– volume: 41
  start-page: 359
  issue: 138
  year: 1995
  end-page: 372
  ident: 7
  article-title: Dry-flowing avalanche run-up and run-out
– volume: 216
  start-page: 448
  issue: 2
  year: 2010
  end-page: 457
  ident: 11
  article-title: Positive solutions for systems of a nonlinear fourth-order singular semipositone boundary value problems
– volume: 26
  start-page: 998
  issue: 10
  year: 2013
  end-page: 1004
  ident: 36
  article-title: Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers
– volume: 32
  start-page: 411
  issue: 3
  year: 2007
  end-page: 424
  ident: 3
  article-title: Efficient numerical solution of the density profile equation in hydrodynamics
– reference: Berlinet A. Thomas-Agnan C. Reproducing Kernel Hilbert Spaces in Probability and Statistics 2004 Boston, Mass, USA Kluwer Academic Publishers 10.1007/978-1-4419-9096-9 MR2239907
– volume: 219
  start-page: 8938
  issue: 17
  year: 2013
  end-page: 8948
  ident: 26
  article-title: Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method
– volume: 30
  start-page: 289
  issue: 1
  year: 2014
  end-page: 300
  ident: 37
  article-title: A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation
– volume: 53
  start-page: 1429
  issue: 9
  year: 2007
  end-page: 1438
  ident: 15
  article-title: Positive solutions for singular systems of three-point boundary value problems
– volume: 19
  start-page: 808
  issue: 8
  year: 2006
  end-page: 813
  ident: 20
  article-title: Representation of the exact solution for a kind of nonlinear partial differential equation
– volume: 2012
  year: 2012
  end-page: 16
  ident: 25
  article-title: Application of reproducing kernel method for solving nonlinear Fredholm-Volterra integrodifferential equations
– volume: 25
  start-page: 818
  issue: 5
  year: 2012
  end-page: 823
  ident: 35
  article-title: A reproducing kernel method for solving nonlocal fractional boundary value problems
– reference: Cui M. Lin Y. Nonlinear Numerical Analysis in the Reproducing Kernel Space 2009 New York, NY, USA Nova Science MR2502102
– volume: 255
  start-page: 97
  year: 2014
  end-page: 105
  ident: 38
  article-title: A numerical method for singularly perturbed turning point problems with an interior layer
– reference: Daniel A. Reproducing Kernel Spaces and Applications 2003 Basel, Switzerland Springer 10.1007/978-3-0348-8077-0 MR2019345
– volume: 148
  start-page: 561
  issue: 2
  year: 2004
  end-page: 570
  ident: 6
  article-title: Analytical and numerical treatment of a singular initial value problem in avalanche modeling
– volume: 2014
  year: 2014
  end-page: 10
  ident: 28
  article-title: A numerical iterative method for solving systems of first-order periodic boundary value problems
– volume: 8
  start-page: 2809
  issue: 6
  year: 2014
  end-page: 2821
  ident: 10
  article-title: An optimization algorithm for solving systems of singular boundary value problems
– volume: 2012
  year: 2012
  end-page: 25
  ident: 9
  article-title: Solving singular two-point boundary value problems using continuous genetic algorithm
– ident: 22
  doi: 10.1016/j.amc.2014.06.063
– ident: 17
  doi: 10.1007/978-1-4419-9096-9
– ident: 2
  doi: 10.1016/j.apnum.2005.04.012
– ident: 9
  doi: 10.1155/2012/205391
– ident: 28
  doi: 10.1155/2014/135465
– ident: 25
  doi: 10.1155/2012/839836
– ident: 38
  doi: 10.1016/j.cam.2013.04.040
– ident: 3
  doi: 10.1007/s10915-007-9141-0
– ident: 31
– ident: 20
  doi: 10.1016/j.aml.2005.10.010
– ident: 5
  doi: 10.1016/j.jmaa.2006.10.006
– ident: 18
  doi: 10.1007/978-3-0348-8077-0
– ident: 1
  doi: 10.1006/jcph.1999.6262
– volume: 41
  start-page: 359
  issue: 138
  year: 1995
  ident: 7
  publication-title: Journal of Glaciology
  doi: 10.1017/S0022143000016233
– year: 1982
  ident: 19
– ident: 11
  doi: 10.1016/j.amc.2010.01.038
– volume: 8
  start-page: 857
  year: 2015
  ident: 29
  publication-title: Journal of Computational Analysis and Applications
– ident: 37
  doi: 10.1002/num.21809
– ident: 34
  doi: 10.1016/j.amc.2013.03.123
– ident: 24
  doi: 10.1155/2013/832074
– year: 2009
  ident: 16
– ident: 32
  doi: 10.1016/j.amc.2007.03.016
– ident: 36
  doi: 10.1016/j.aml.2013.05.006
– volume: 2008
  issue: 29
  year: 2008
  ident: 21
  publication-title: Electronic Journal of Differential Equations
– ident: 33
  doi: 10.1016/s0096-3003(02)00370-3
– ident: 30
  doi: 10.1155/2014/758195
– volume: 16
  start-page: 750
  issue: 4
  year: 2014
  ident: 27
  publication-title: Journal of Computational Analysis and Applications
– ident: 6
  doi: 10.1016/s0096-3003(02)00919-0
– ident: 8
  doi: 10.1137/1.9781611971231
– ident: 26
  doi: 10.1016/j.amc.2013.03.006
– ident: 14
  doi: 10.1016/j.jmaa.2006.06.053
– ident: 12
  doi: 10.1016/j.amc.2008.12.019
– ident: 23
  doi: 10.1016/j.amc.2014.04.057
– ident: 13
  doi: 10.1016/j.jmaa.2006.06.054
– ident: 15
  doi: 10.1016/j.camwa.2006.07.014
– ident: 10
  doi: 10.12785/amis/080617
– ident: 35
  doi: 10.1016/j.aml.2011.10.025
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Snippet The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order...
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SubjectTerms Algorithms
Approximation
Boundary conditions
Boundary value problems
Dynamical systems
Evolutionary algorithms
Kernel functions
Kernels
Mathematical analysis
Mathematical models
Mathematical problems
Nonlinear dynamics
Nonlinear systems
Numerical methods
Series (mathematics)
Systems analysis
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Title Reproducing Kernel Algorithm for the Analytical-Numerical Solutions of Nonlinear Systems of Singular Periodic Boundary Value Problems
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