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

Contributors: Aceto, Lidia, Conte, Dajana, Pagano, Giovanni

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

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

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

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

Authors: Yahui Wang, Guozeng Yang, Cheng Guo, Lijun Hu

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

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, Harish Kumar, Dinshaw S. Balsara

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

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

Contributors: University of Zurich, Barsukow, Wasilij

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, Seungyoon Kang, Junseok Kim

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, Dalcin, Lisandro, Schlottke-Lakemper, Michael Alexander, Gassner, Gregor J., Parsani, Matteo

Contributors: Extreme Computing Research Center (ECRC), Computer Electrical and Mathematical Science and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia, Extreme Computing Research Center, Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Applied Mathematics and Computational Science Program, Physical Science and Engineering (PSE) Division

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

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

Authors: Sujoy Basak, Arpit Babbar, Harish Kumar, Praveen Chandrashekar

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

Entropy stable hydrostatic reconstruction schemes for shallow water systems

Authors: Patrick Ersing, Sven Goldberg, Andrew R. Winters

Source: Journal of Computational Physics. 527:113802

Subject Terms: Hydrology, hydrography, oceanography, Spectral methods applied to problems in fluid mechanics, Beräkningsmatematik, entropy stability, positivity-preserving, discontinuous Galerkin method, First-order nonlinear hyperbolic equations, Positivity-preserving, wetting and drying, FOS: Mathematics, Mathematics - Numerical Analysis, multilayer shallow water equations, Method of lines for initial value and initial-boundary value problems involving PDEs, 65M12, 65M20, 65M70, 76M22, 35L60, 86A05, Multilayer shallow water equations, Numerical Analysis (math.NA), Entropy stability, 6. Clean water, Computational Mathematics, Discontinuous Galerkin method, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Wetting and drying, Well-balanced, First-order hyperbolic systems, well-balanced, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2406.14119
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-211521

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

High-order accurate adjoint-state methods for three-dimensional high-resolution first-arrival traveltime tomography

Authors: Bingqian Si, Aaron Philip, Yuxiao Wei, Jianliang Qian

Source: Journal of Computational Physics. 524:113715

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, eikonal equation, traveltime tomography, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Hamilton-Jacobi, adjoint-state method, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Lax-Friedrichs, weighted essentially non-oscillatory schemes

File Description: application/xml

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

Ruminated Tensor Decomposition algorithm for solving inviscid Burgers' equation: Ruminated tensor decomposition algorithm for solving inviscid Burgers' equation

Authors: Tang, Shaoqiang, Xu, Hongjian

Source: Journal of Computational Physics. 523:113663

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, ruminated tensor decomposition, Numerical methods for low-rank matrix approximation, matrix compression, sensitivity to initial guesses, inviscid Burgers' equation, Godunov's method, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, loss function

File Description: application/xml

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

Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness

Authors: Lindstrom, Michael R, Bertozzi, Andrea L

Source: Mathematical Models and Methods in Applied Sciences, vol 30, iss 10

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Finite difference methods for boundary value problems involving PDEs, Agent-based model, Numerical and Computational Mathematics, Applied Mathematics, 1. No poverty, Homelessness, Computational methods for problems pertaining to game theory, economics, and finance, nonlocal PDE, agent-based model, Maximum principles in context of PDEs, PDEs in connection with game theory, economics, social and behavioral sciences, 13. Climate action, Models of societies, social and urban evolution, Heterogeneous agent models, Nonlinear parabolic equations, nonlinear diffusion, solution properties, Stability in context of PDEs, homelessness, Periodic solutions to PDEs

File Description: application/xml; application/pdf

Access URL: https://www.worldscientific.com/doi/pdf/10.1142/S0218202520400114
https://escholarship.org/content/qt2jf0d2wf/qt2jf0d2wf.pdf?t=qhvs96
https://www.worldscientific.com/doi/abs/10.1142/S0218202520400114
https://escholarship.org/uc/item/2jf0d2wf
https://escholarship.org/uc/item/2jf0d2wf

A Group of CFL-Dependent Flux-Limiters to Control the Numerical Dissipation in Multi-stage Unsteady Calculation: A group of CFL-dependent flux-limiters to control the numerical dissipation in multi-stage unsteady calculation

Authors: Jiong Ren, Gang Wang, Mingsheng Ma

Source: Journal of Scientific Computing. 81:186-216

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, TVD criterion, high resolution, numerical dissipation, Gas dynamics (general theory), Euler equations, Shock waves and blast waves in fluid mechanics, 01 natural sciences, CFL-dependent flux-limiter, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Error bounds for initial value and initial-boundary value problems involving PDEs, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Hyperbolic conservation laws, Supersonic flows, 0103 physical sciences, 0101 mathematics, First-order hyperbolic equations

File Description: application/xml

Access URL: https://zbmath.org/7129355
https://doi.org/10.1007/s10915-019-01010-4
https://dblp.uni-trier.de/db/journals/jscic/jscic81.html#RenWM19
https://link.springer.com/article/10.1007/s10915-019-01010-4
https://doi.org/10.1007/s10915-019-01010-4

Remarks on a new particle method

Authors: Després, Bruno, Remmerswaal, Ronald

Source: Journal of Computational Physics. 523:113662

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, Particle methods and lattice-gas methods, Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs, Finite volume methods applied to problems in fluid mechanics

File Description: application/xml