Search Results - Method of lines for initial value and initial-boundary value problems involving PDEs~

Analysis for implicit and implicit-explicit ADER and DeC methods for ordinary differential equations, advection-diffusion and advection-dispersion equations

Authors: Philipp Öffner Louis Petri Davide Torlo

Source: Applied Numerical Mathematics. 212:110-134

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, advection-diffusion, implicit-explicit methods, deferred correction, ADER, advection-dispersion, 65M06, 65M20, 65L05, 65L06, 65L07, Numerical Analysis (math.NA), stability, Numerical methods for initial value problems involving ordinary differential equations, Advection-diffusion, Advection-dispersion, Deferred correction, Implicit-explicit methods, Stability, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for ordinary differential equations

File Description: application/xml

Access URL: http://arxiv.org/abs/2404.18626
https://hdl.handle.net/11573/1747980
https://doi.org/10.1016/j.apnum.2024.12.013

Modified TASE Runge–Kutta Methods for Integrating Stiff Differential Equations: Modified TASE Runge-Kutta methods for integrating stiff differential equations

Authors: Lidia Aceto Dajana Conte Giovanni Pagano et al.

Contributors: Lidia Aceto Dajana Conte Giovanni Pagano et al.

Source: SIAM Journal on Scientific Computing. 47:A1652-A1680

Subject Terms: TASE preconditioner, Method of lines for initial value and initial-boundary value problems involving PDEs, Runge-Kutta methods, numerical methods for PDEs, TASE preconditioners, Runge–Kutta methods, stiff problems, W-methods, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Numerical methods for PDE, Numerical methods for stiff equations, Runge-Kutta method, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for ordinary differential equations, stiff problem

File Description: application/xml; ELETTRONICO

Access URL: https://zbmath.org/8037172
https://doi.org/10.1137/24m1667336
https://hdl.handle.net/11588/1001148
https://epubs.siam.org/doi/10.1137/24M1667336
https://hdl.handle.net/11588/1001148
https://doi.org/10.1137/24M1667336
https://epubs.siam.org/doi/10.1137/24M1667336

Multiple Relaxation Exponential Runge–Kutta Methods for the Nonlinear Schrödinger Equation: Multiple relaxation exponential Runge-Kutta methods for the nonlinear Schrödinger equation

Authors: Dongfang Li Xiaoxi Li

Source: SIAM Journal on Numerical Analysis. 62:2719-2744

Subject Terms: Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Method of lines for initial value and initial-boundary value problems involving PDEs, high-order accuracy, NLS equations (nonlinear Schrödinger equations), Time-dependent Schrödinger equations and Dirac equations, structure-preserving methods, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, relaxation technique, nonlinear Schrödinger equation, exponential Runge-Kutta methods, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: https://zbmath.org/7963013
https://doi.org/10.1137/23m1606034

Optimizing Coarse Propagators in Parareal Algorithms: Optimizing coarse propagators in parareal algorithms

Authors: Bangti Jin Qingle Lin Zhi Zhou

Source: SIAM Journal on Scientific Computing. 47:A735-A761

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, convergence factor, single step integrator, Parallel numerical computation, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Error bounds for initial value and initial-boundary value problems involving PDEs, parareal algorithm, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, parabolic problems

File Description: application/xml

Access URL: http://arxiv.org/abs/2311.15320
https://zbmath.org/8010023
https://doi.org/10.1137/23m1619733

A Semi-discrete Active Flux Method for the Euler Equations on Cartesian Grids: A semi-discrete active flux method for the Euler equations on Cartesian grids

Authors: Abgrall, Remi Barsukow, Wasilij Klingenberg, Christian et al.

Contributors: Abgrall, Remi Barsukow, Wasilij Klingenberg, Christian et al.

Source: Journal of Scientific Computing. 102

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Keywords Compressible Euler equations · Active flux · High, Finite volume methods for boundary value problems involving PDEs, Finite volume methods applied to problems in fluid mechanics, Numerical Analysis (math.NA), Euler equations, compressible Euler equations, 1712 Software, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, 10123 Institute of Mathematics, 510 Mathematics, 2604 Applied Mathematics, Finite volume methods for initial value and initial-boundary value problems involving PDEs, active flux, order methods Mathematics Subject Classification 65M08 · 65M20 · 65M70 · 76M12, high-order methods, 65M08, 65M20, 65M70, 76M12, 2200 General Engineering, Existence, uniqueness, and regularity theory for incompressible inviscid fluids, FOS: Mathematics, Mathematics - Numerical Analysis, 2614 Theoretical Computer Science, 2612 Numerical Analysis, 2605 Computational Mathematics, 1703 Computational Theory and Mathematics

File Description: application/xml; Abgrall2025_ASemiDiscreteActiveFluxMethod.pdf - application/pdf

Access URL: http://arxiv.org/abs/2310.00683
https://zbmath.org/7969181
https://doi.org/10.1007/s10915-024-02749-1

Threshold stability analysis of an unconditionally positivity-preserving numerical method for a nonlinear age-structured diffusive HIV model with spatial coefficients

Authors: Zhang, Meng Liu, Xing Yang, Shiyuan

Source: Zeitschrift für angewandte Mathematik und Physik. 76

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Finite difference methods for boundary value problems involving PDEs, Medical epidemiology, age-structured model, Epidemiology, PDEs in connection with biology, chemistry and other natural sciences, Positive solutions to PDEs, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, numerical basic reproduction number, numerical stability, numerical threshold stability, Finite difference methods for initial value and initial-boundary value problems involving PDEs, HIV model, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Computational methods for problems pertaining to biology

File Description: application/xml

Access URL: https://zbmath.org/7975303
https://doi.org/10.1007/s00033-024-02416-3

Fast numerical algorithm for the reaction-diffusion equations using an interpolating method

Authors: Sungha Yoon Chaeyoung Lee Soobin Kwak et al.

Source: Computational and Applied Mathematics. 44

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, interpolating, reaction-diffusion equations, Reaction-diffusion equations, splitting method, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics: On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics

Authors: Ranocha, Hendrik Winters, Andrew R. Castro, Hugo Guillermo et al.

Contributors: Ranocha, Hendrik Winters, Andrew R. Castro, Hugo Guillermo et al.

Source: Communications on applied mathematics and computation : CAMC 7(1), 3-39 (2023). doi:10.1007/s42967-023-00264-y

Subject Terms: ADAPTIVITY IN SPACE AND TIME, Spectral methods applied to problems in fluid mechanics, Beräkningsmatematik, FOS: Physical sciences, 01 natural sciences, COMPRESSIBLE FLUID DYNAMICS, Explicit Runge-Kutta (RK) methods, Step size control, Compressible fluid dynamics, Adaptivity in space and time, Shock capturing, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, compressible fluid dynamics, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, SHOCK CAPTURING, ddc:510, Method of lines for initial value and initial-boundary value problems involving PDEs, shock capturing, STEP SIZE CONTROL, Initial-boundary value problems for first-order hyperbolic systems, Numerical Analysis (math.NA), Computational Physics (physics.comp-ph), EXPLICIT RUNGE-KUTTA (RK) METHODS, step size control, 65L06, 65M20, 65M70, 76M10, 76M22, 76N99, 35L50, Computational Mathematics, explicit Runge-Kutta (RK) methods, Compressible fluids and gas dynamics, adaptivity in space and time, Physics - Computational Physics, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Finite element methods applied to problems in fluid mechanics

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2209.07037
https://zbmath.org/7996399
https://doi.org/10.1007/s42967-023-00264-y
https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-1137215
https://opus.bibliothek.uni-augsburg.de/opus4/files/113721/113721.pdf
https://doi.org/10.1007/s42967-023-00264-y
https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/113721
http://hdl.handle.net/11336/213686
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-194018
http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-161080
https://elib.uni-stuttgart.de/handle/11682/16108
https://doi.org/10.18419/opus-16089
https://publications.rwth-aachen.de/record/962377

Deferred Correction Methods for Initial Boundary Value Problems: Deferred correction methods for initial boundary value problems

Authors: Wendy Kress Bertil Gustafsson

Source: Journal of Scientific Computing. 17:241-251

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, convergence, initial boundary value problems, implicit difference methods, method of lines, deferred correction, stability, 01 natural sciences, Error bounds for initial value and initial-boundary value problems involving PDEs, error estimates, high-order methods, Nonlinear parabolic equations, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, numerical experiments

File Description: application/xml

Access URL: https://zbmath.org/1784235
https://doi.org/10.1023/a:1015113017248

Entropy Stable Finite Difference Schemes for Chew, Goldberger and Low Anisotropic Plasma Flow Equations: Entropy stable finite difference schemes for Chew, Goldberger and Low anisotropic plasma flow equations

Authors: Chetan Singh Anshu Yadav Deepak Bhoriya et al.

Source: Journal of Scientific Computing. 102

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, symmetrization, entropy stability, Numerical Analysis (math.NA), PDEs in connection with fluid mechanics, Shock waves and blast waves in fluid mechanics, Finite difference methods applied to problems in fluid mechanics, 65M06, 65M12, 65M20, 76P99 and 76W05, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Ionized gas flow in electromagnetic fields, plasmic flow, FOS: Mathematics, Magnetohydrodynamics and electrohydrodynamics, Mathematics - Numerical Analysis, higher-order finite difference schemes, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Weak solutions to PDEs, CGL equations

File Description: application/xml

Access URL: http://arxiv.org/abs/2406.04783
https://zbmath.org/7975324
https://doi.org/10.1007/s10915-024-02763-3

Improved sixth-order WENO scheme based on the numerical flux and smoothness indicators of modified stencils

Authors: Yahui Wang Guozeng Yang Cheng Guo et al.

Source: Computational and Applied Mathematics. 44

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, hyperbolic conservation law, Finite volume methods for initial value and initial-boundary value problems involving PDEs, WENO scheme, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, modified stencils, sixth-order accuracy

File Description: application/xml

Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems

Authors: M. P. Calvo C. Palencia

Source: Mathematics of Computation. 71:1529-1544

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Abstract parabolic equations, numerical example, Linear differential equations in abstract spaces, Banach space, Numerical solutions to equations with linear operators, Runge-Kutta method, order reduction, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Numerical methods for initial value problems involving ordinary differential equations, abstract initial boundary value problems, 01 natural sciences

File Description: application/xml

Access URL: https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01362-X/S0025-5718-01-01362-X.pdf
https://zbmath.org/1802726
https://doi.org/10.1090/s0025-5718-01-01362-x
http://ui.adsabs.harvard.edu/abs/2002MaCom..71.1529C/abstract
https://www.ams.org/journals/mcom/2002-71-240/S0025-5718-01-01362-X/
https://doi.org/10.1090/S0025-5718-01-01362-X
https://dblp.uni-trier.de/db/journals/moc/moc71.html#CalvoP02
https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01362-X/S0025-5718-01-01362-X.pdf

The second-order initial/boundary value problem: Supraconvergence of regridding methods: The second-order initial/boundary value problem: supraconvergence of regridding methods

Authors: José Augusto Ferreira

Source: Applied Numerical Mathematics. 13:69-81

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, convergence, supraconvergence, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, regridding methods, method of lines, linear parabolic initial-boundary value problem, Initial value problems for second-order parabolic equations, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, 01 natural sciences

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/016892749390132B

Runge-Kutta methods without order reduction for linear initial boundary value problems

Authors: Isaías Alonso-Mallo

Source: Numerische Mathematik. 91:577-603

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, numerical examples, Linear differential equations in abstract spaces, linear initial boundary value problem, semidiscretization, Runge-Kutta method, Initial value problems for second-order parabolic equations, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1773395
https://doi.org/10.1007/s002110100332
https://link.springer.com/article/10.1007%2Fs002110100332
https://dblp.uni-trier.de/db/journals/nm/nm91.html#Alonso-Mallo02
https://rd.springer.com/article/10.1007/s002110100332

Bound preserving Lax-Wendroff flux reconstruction method for special relativistic hydrodynamics

Authors: Sujoy Basak Arpit Babbar Harish Kumar et al.

Source: Journal of Computational Physics. 527:113815

Subject Terms: Quantum hydrodynamics and relativistic hydrodynamics, Method of lines for initial value and initial-boundary value problems involving PDEs, Finite volume methods for initial value and initial-boundary value problems involving PDEs, admissibility preservation, FOS: Mathematics, G.1.8, Lax-Wendroff flux reconstruction, Finite volume methods applied to problems in fluid mechanics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), relativistic hydrodynamics, 65M60

File Description: application/xml

Access URL: http://arxiv.org/abs/2409.15805

Extensions and investigations of space‐time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms: Extensions and investigations of space-time generalized Riemann problems numerical schemes for linear systems of conservation laws with source terms

Authors: Rodolphe Turpault

Source: Numerical Methods for Partial Differential Equations. 40

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Error bounds for initial value and initial-boundary value problems involving PDEs, space-time generalized Riemann problems, Hyperbolic conservation laws, very high order numerical schemes, 0103 physical sciences, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, 0101 mathematics, large time steps, linear hyperbolic systems of conservation laws with source terms, 01 natural sciences, First-order hyperbolic systems

File Description: application/xml

Unconditional convergence of some Crank-Nicolson LOD methods for initial-boundary value problems: Unconditional convergence of some Crank-Nicolson lod methods for initial- boundary value problems

Authors: Willem Hundsdorfer

Source: Mathematics of Computation. 58:35-53

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Crank-Nicolson lod methods, splitting methods, LOD methods, stiff systems, locally one-dimensional methods, order reduction, Multiple scale methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, Discretization in space, global error, unconditional convergence, Error bounds for initial value and initial-boundary value problems involving PDEs, consistency order, Nonlinear parabolic equations, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: https://www.ams.org/mcom/1992-58-197/S0025-5718-1992-1106972-8/S0025-5718-1992-1106972-8.pdf
https://ir.cwi.nl/pub/2353/2353D.pdf
https://www.ams.org/mcom/1992-58-197/S0025-5718-1992-1106972-8/S0025-5718-1992-1106972-8.pdf
https://ir.cwi.nl/pub/5721/5721D.pdf
https://www.narcis.nl/publication/RecordID/oai%3Acwi.nl%3A2353
https://ir.cwi.nl/pub/5721
https://www.ams.org/journals/mcom/1992-58-197/S0025-5718-1992-1106972-8/home.html
https://ui.adsabs.harvard.edu/abs/1992MaCom..58...35H/abstract

The Runge–Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws: The Runge-Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws

Authors: Qifan Chen Zheng Sun Yulong Xing

Source: Journal of Computational Physics. 523:113654

Subject Terms: Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Method of lines for initial value and initial-boundary value problems involving PDEs, 65M60, 65M12, 65M20, 65L06, Runge-Kutta method, discontinuous Galerkin method, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, hyperbolic conservation laws, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, stage-dependent polynomial spaces, Fourier-type analysis

File Description: application/xml

Access URL: http://arxiv.org/abs/2402.15150

Many-Stage Optimal Stabilized Runge–Kutta Methods for Hyperbolic Partial Differential Equations: Many-stage optimal stabilized Runge-Kutta methods for hyperbolic partial differential equations

Authors: Döhring, Daniel Gassner, Gregor J. Torrilhon, Manuel

Source: Journal of scientific computing 99(1), 28 (2024). doi:10.1007/s10915-024-02478-5

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Numerical computation of eigenvalues and eigenvectors of matrices, Numerical optimization and variational techniques, Runge-Kutta methods, method of lines, FOS: Physical sciences, Numerical Analysis (math.NA), Mathematical Physics (math-ph), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDE constrained optimization (numerical aspects), 65L06, 65M20, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, absolute stability, Numerical computation using splines, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Best approximation, Chebyshev systems, Mathematics - Classical Analysis and ODEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, initial value problems, Mathematics - Numerical Analysis, Mathematical Physics

File Description: application/xml

Access URL: http://arxiv.org/abs/2402.12140
https://zbmath.org/7823279
https://doi.org/10.1007/s10915-024-02478-5
https://publications.rwth-aachen.de/record/1006130

Spectral-fractional step Runge–Kutta discretizations for initial boundary value problems with time dependent boundary conditions: Spectral-fractional step Runge-Kutta discretizations for initial boundary value problems with time dependent boundary conditions

Authors: B. Cano Isaías Alonso-Mallo J. C. Jorge

Source: Mathematics of Computation. 73:1801-1825

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, numerical examples, convergence, semidiscretization, spectral method, order reduction, 01 natural sciences, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, fractional step Runge-Kutta method, Error bounds for initial value and initial-boundary value problems involving PDEs, initial boundary value problem, local error, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Initial value problems for second-order parabolic equations, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, fully discretization scheme

File Description: application/xml

Access URL: https://www.ams.org/mcom/2004-73-248/S0025-5718-04-01660-6/S0025-5718-04-01660-6.pdf
https://zbmath.org/2091005
https://doi.org/10.1090/s0025-5718-04-01660-6
https://www.ams.org/mcom/2004-73-248/S0025-5718-04-01660-6/S0025-5718-04-01660-6.pdf
https://ui.adsabs.harvard.edu/abs/2004MaCom..73.1801A/abstract
https://www.ams.org/journals/mcom/2004-73-248/S0025-5718-04-01660-6/home.html
https://dblp.uni-trier.de/db/journals/moc/moc73.html#Alonso-MalloCJ04