Search Results - Finite difference methods for initial value and initial-boundary value problems involving PDEs*

A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids

Authors: Meijie Kong Hongfei Fu

Source: Fractional Calculus and Applied Analysis. 27:3446-3476

Subject Terms: Iterative numerical methods for linear systems, fractional block-centered finite difference method, nonuniform grids, Mathematics - Analysis of PDEs, space-fractional diffusion equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), fast matrix-vector multiplication, Fractional partial differential equations, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2312.10577
https://zbmath.org/7996702
https://doi.org/10.1007/s13540-024-00346-5

An Upwind-Block-Centered Multistep Difference Method for a Semiconductor Device and Numerical Analysis: An upwind-block-centered multistep difference method for a semiconductor device and numerical analysis

Authors: Yuan, Yirang Li, Changfeng Song, Huailing

Source: Advances in Applied Mathematics and Mechanics. 17:706-731

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Statistical mechanics of semiconductors, Finite difference methods for initial value and initial-boundary value problems involving PDEs, numerical computation, local conservation of mass, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, upwind block-centered multistep difference, three-dimensional semiconductor device, convergence analysis

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Implicit integration factor method coupled with Padé approximation strategy for nonlocal Allen-Cahn equation

Authors: Yuxin Zhang Hengfei Ding

Source: Applied Numerical Mathematics. 213:88-107

Subject Terms: energy stability, implicit integration factor method, Smoothness and regularity of solutions to PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, discrete maximum principle, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Riesz derivative

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Access URL: http://arxiv.org/abs/2502.02089
https://zbmath.org/8034919
https://doi.org/10.1016/j.apnum.2025.02.019

A FAST PARALLEL DIFFERENCE METHOD FOR SOLVING THE TIME-FRACTIONAL GENERALIZED FISHER EQUATION: A fast parallel difference method for solving the time-fractional generalized Fisher equation

Authors: Chai, Longtao Wu, Lifei Yang, Xiaozhong

Source: Journal of Applied Analysis & Computation. 15:1216-1240

Subject Terms: time-fractional generalized Fisher (TFGF) equation, parallel computing, Finite difference methods for initial value and initial-boundary value problems involving PDEs, fast \(\mathrm{L}1\) approximation, stability and convergence, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, alternating segment difference scheme

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Access URL: https://zbmath.org/8011300
https://doi.org/10.11948/20240159

Structure-preserving finite element methods for computing dynamics of rotating Bose–Einstein condensates: Structure-preserving finite element methods for computing dynamics of rotating Bose-Einstein condensates

Authors: Li, Meng Wang, Junjun Guan, Zhen et al.

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 59:519-552

Subject Terms: NLS equations (nonlinear Schrödinger equations), structure-preserving, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, rotating Bose-Einstein condensate, Error bounds for initial value and initial-boundary value problems involving PDEs, Time-dependent Schrödinger equations and Dirac equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Quantum dynamics and nonequilibrium statistical mechanics (general), Statistical mechanics of superfluids, FOS: Mathematics, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, finite element methods, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Gross-Pitaevskii equation, angular momentum rotation

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Access URL: http://arxiv.org/abs/2405.16827
https://zbmath.org/7989674
https://doi.org/10.1051/m2an/2024067

An Energy-Stable Parametric Finite Element Method for the Planar Willmore Flow: An energy-stable parametric finite element method for the planar Willmore flow

Authors: Weizhu Bao Yifei Li

Source: SIAM Journal on Numerical Analysis. 63:103-121

Subject Terms: geometric identity, parametric finite element method, Finite difference methods for initial value and initial-boundary value problems involving PDEs, energy-stable, Nonlinear parabolic equations, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Global surface theory (convex surfaces à la A. D. Aleksandrov), Willmore flow

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Access URL: http://arxiv.org/abs/2401.13274

Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions: Spatial-temporal adaptive-order positivity-preserving WENO finite difference scheme with relaxed CFL condition for Euler equations with extreme conditions

Authors: Li, Jia-Le Don, Wai-Sun Wang, Cai-Feng et al.

Source: Advances in Applied Mathematics and Mechanics. 17:804-839

Subject Terms: relaxed CFL condition, WENO, Hyperbolic equations on manifolds, Hyperbolic conservation laws, Finite difference methods for initial value and initial-boundary value problems involving PDEs, positivity-preserving, adaptive-CFL and adaptive-order method, extreme problems

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Access URL: https://zbmath.org/8033903
https://doi.org/10.4208/aamm.oa-2023-0306

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

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

A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces: A meshfree RBF-FD constant along normal method for solving PDEs on surfaces

Authors: Víctor Bayona Argyrios Petras Cécile Piret et al.

Contributors: Víctor Bayona Argyrios Petras Cécile Piret et al.

Source: e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid
Universidad Carlos III de Madrid (UC3M)

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Matemáticas, Closest point method, Meshfree, Numerical Analysis (math.NA), meshfree, Numerical differentiation, Approximation by polynomials, Spline approximation, High-order methods, Numerical interpolation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, high-order methods, PDEs on surfaces, FOS: Mathematics, RBF-FD, Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Interpolation in approximation theory, Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs, closest point method

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Access URL: http://arxiv.org/abs/2412.14761
https://hdl.handle.net/10016/46963

Eigenvalue analysis and applications of the Legendre dual-Petrov-Galerkin methods for initial value problems

Authors: Desong Kong Jie Shen Li-Lian Wang et al.

Source: Advances in Computational Mathematics. 50

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Asymptotic distributions of eigenvalues in context of PDEs, eigenvalue distributions, spectral method in time, QZ decomposition, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, matrix diagonalisation, 01 natural sciences, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), KdV equations (Korteweg-de Vries equations), Bessel and generalised Bessel polynomials, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, 65M70, 65L15, 65F15, 33C45, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Mathematics - Numerical Analysis, 0101 mathematics, Numerical solution of eigenvalue problems involving ordinary differential equations, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Legendre dual Petrov-Galerkin methods

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Access URL: http://arxiv.org/abs/2211.10599
https://zbmath.org/7932062
https://doi.org/10.1007/s10444-024-10190-z

New Time Domain Decomposition Methods for Parabolic Optimal Control Problems II: Neumann–Neumann Algorithms: New time domain decomposition methods for parabolic optimal control problems. II: Neumann-Neumann algorithms

Authors: Martin J. Gander Liu-Di Lu

Source: SIAM Journal on Numerical Analysis. 62:2588-2610

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Controllability, parallel in time, time domain decomposition, 65M12, 65M55, 65Y05, Parallel numerical computation, parabolic optimal control problems, Numerical Analysis (math.NA), PDE constrained optimization (numerical aspects), 01 natural sciences, convergence analysis, Neumann-Neumann algorithm, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Optimization and Control (math.OC), Approximation by arbitrary linear expressions, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2401.15522
https://zbmath.org/7957568
https://doi.org/10.1137/24m1634424

Numerical treatment of singularly perturbed turning point problems with delay in time

Authors: Singh, Satpal Kumar, Devendra Vigo-Aguiar, J.

Source: Journal of Mathematical Chemistry. 63:1035-1064

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Shishkin mesh, Stability and convergence of numerical methods for boundary value problems involving PDEs, turning point, time lag, Spline approximation, Error bounds for initial value and initial-boundary value problems involving PDEs, parameter-uniform convergence, Second-order parabolic equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for ordinary differential equations, delay differential equation, Singular perturbations, turning point theory, WKB methods for ordinary differential equations, splines, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, singular perturbation, Singular perturbations in context of PDEs

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Access URL: https://zbmath.org/8018422
https://doi.org/10.1007/s10910-025-01707-y

Stabilization of loosely coupled schemes for 0D–3D fluid–structure interaction problems with application to cardiovascular modelling: Stabilization of loosely coupled schemes for 0D-3D fluid-structure interaction problems with application to cardiovascular modelling

Authors: Regazzoni, Francesco

Source: Numerische Mathematik. 157:249-306

Subject Terms: Physiological flow, cardiovascular modelling, Biological applications of optics and electromagnetic theory, PDEs in connection with biology, chemistry and other natural sciences, Finite difference methods for initial value and initial-boundary value problems involving PDEs, fluid-structure interaction, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Physiological flows, Biomechanical solid mechanics, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

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Access URL: https://zbmath.org/7978173
https://doi.org/10.1007/s00211-025-01452-z

Step-by-step time discrete Physics-Informed Neural Networks with application to a sustainability PDE model: Step-by-step time discrete physics-informed neural networks with application to a sustainability PDE model

Authors: Valentino C. Pagano G. Conte D. et al.

Source: Mathematics and Computers in Simulation. 230:541-558

Subject Terms: Scientific machine learning, deep artificial neural networks, scientific machine learning, Stiff problems, Nonlinear sustainability PDE model, Implicit Euler and Crank–Nicolson methods, Deep artificial neural networks, Time discrete PINNs, Dye-sensitized solar cells, Numerical methods for initial value problems involving ordinary differential equations, nonlinear sustainability PDE model, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, time discrete PINNs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, implicit Euler and Crank-Nicolson methods, Numerical investigation of stability of solutions to ordinary differential equations, dye-sensitized solar cells, stiff problems, Artificial neural networks and deep learning

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Access URL: https://hdl.handle.net/11588/995692
https://www.sciencedirect.com/science/article/pii/S0378475424004403

A review of temporal and spatial dispersions of linear and quadratic finite elements in linear elastic wave propagation problems

Authors: Kolman, R. (Radek) Okrouhlík, M. (Miloslav) Kruisová, A. (Alena)

Source: Proceedings of the Estonian Academy of Sciences, Vol 73, Iss 3, Pp 279-316 (2024)

Subject Terms: Finite element methods applied to problems in solid mechanics, Linear elasticity with initial stresses, Science, elastic wave propagation, finite element method, direct time integration, spurious oscillations, Finite difference methods applied to problems in solid mechanics, Error bounds for initial value and initial-boundary value problems involving PDEs, Vibrations in dynamical problems in solid mechanics, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Strings, dispersion, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Linear waves in solid mechanics, PDEs in connection with mechanics of deformable solids, Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids

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Access URL: https://hdl.handle.net/11104/0358061

An inverse problem of identifying two coefficients in a time-fractional reaction diffusion system

Authors: Srati, Mohammed Oulmelk, Abdessamad Afraites, Lekbir et al.

Source: Discrete and Continuous Dynamical Systems - S. 18:113-147

Subject Terms: inverse parameter problem, Inverse problems in optimal control, time-fractional diffusion system, optimal control problem, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Sensitivity, stability, well-posedness, Existence theories for optimal control problems involving partial differential equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, stability analysis, Functional-differential equations with fractional derivatives

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Access URL: https://zbmath.org/7962675
https://doi.org/10.3934/dcdss.2023054

Exact symmetry conservation and automatic mesh refinement in discrete initial boundary value problems

Authors: Alexander Rothkopf W.A. Horowitz Jan Nordström

Source: Journal of Computational Physics. 524:113686

Subject Terms: High Energy Physics - Theory, Beräkningsmatematik, High Energy Physics - Lattice (hep-lat), FOS: Physical sciences, Numerical Analysis (math.NA), Computational Physics (physics.comp-ph), Computational Mathematics, High Energy Physics - Lattice, High Energy Physics - Theory (hep-th), Finite difference methods for initial value and initial-boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Physics - Computational Physics

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Access URL: http://arxiv.org/abs/2404.18676
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-210826

Implementation of the ADMM approach to constrained optimal control problem with a nonlinear time-fractional diffusion equation

Authors: Oulmelk, Abdessamad Srati, Mohammed Afraites, Lekbir et al.

Source: Discrete and Continuous Dynamical Systems - S. 18:15-42

Subject Terms: inverse parameter problem, Inverse problems in optimal control, optimal control problem, alternating direction method of multiplier (ADMM), Finite difference methods for initial value and initial-boundary value problems involving PDEs, Existence theories for optimal control problems involving partial differential equations, Stability and convergence of numerical methods for boundary value problems involving PDEs, time-fractional diffusion equation, Functional-differential equations with fractional derivatives, convergence analysis

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Hybrid Approach to Modeling and Evaluating the Structural Features for Patterns of Cultured Bacteria: Hybrid approach to modeling and evaluation of the structural features for patterns of cultured bacteria

Authors: Shevkun, I. A. Maslovskaya, A. G.

Source: Mathematical Models and Computer Simulations. 17:153-161

Subject Terms: fractal dimension, reaction-diffusion model, Reaction-diffusion equations, computational experiment, Finite difference methods for initial value and initial-boundary value problems involving PDEs, stochastic growth mechanism, Developmental biology, pattern formation, pattern, Microbiology, bacterial cultivation, dendrite

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Access URL: https://zbmath.org/8018448
https://doi.org/10.20948/mm-2024-06-04

A parameter uniform numerical method on a Bakhvalov type mesh for singularly perturbed degenerate parabolic convection–diffusion problems: A parameter uniform numerical method on a Bakhvalov type mesh for singularly perturbed degenerate parabolic convection-diffusion problems

Authors: Shashikant Kumar Sunil Kumar Higinio Ramos et al.

Source: GREDOS. Repositorio Institucional de la Universidad de Salamanca
Universidad de Salamanca (USAL)

Subject Terms: 12 Matemáticas, uniform convergence, 01 natural sciences, Bakhvalov mesh, Error bounds for initial value and initial-boundary value problems involving PDEs, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, upwind scheme, Upwind scheme, Finite difference methods for initial value and initial-boundary value problems involving PDEs, degenerate parabolic problem, Degenerate parabolic problem, Uniform convergence, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Singular perturbation, singular perturbation

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Access URL: http://hdl.handle.net/10366/166738