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

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

File Description: application/xml

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

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

Energy stability and error estimate of the RKMK2e scheme for the extended Fisher–Kolmogorov equation: Energy stability and error estimate of the RKMK2e scheme for the extended Fisher-Kolmogorov equation

Authors: Haifeng Wang Yan Wang Hong Zhang et al.

Source: Applied Numerical Mathematics. 212:60-76

Subject Terms: Error bounds for initial value and initial-boundary value problems involving PDEs, global-in-time energy stability, Finite difference methods for initial value and initial-boundary value problems involving PDEs, extended Fisher-Kolmogorov equation, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, error analysis, stabilization RKMK2e scheme

File Description: application/xml

Access URL: https://zbmath.org/8018678
https://doi.org/10.1016/j.apnum.2025.01.014

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

File Description: application/xml

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

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

File Description: application/xml

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

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

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

File Description: application/xml

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

Numerical Approximation of Discontinuous Solutions of the Semilinear Wave Equation: Numerical approximation of discontinuous solutions of the semilinear wave equation

Authors: Jiachuan Cao Buyang Li Yanping Lin et al.

Source: SIAM Journal on Numerical Analysis. 63:214-238

Subject Terms: Smoothness and regularity of solutions to PDEs, high-/low-frequency decomposition, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Numerical Analysis (math.NA), Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Error bounds for initial value and initial-boundary value problems involving PDEs, KdV equations (Korteweg-de Vries equations), error estimates, Numerical interpolation, semilinear wave equation, discontinuous solution, 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, low regularity, Numerical methods for discrete and fast Fourier transforms, numerical approximation

File Description: application/xml

Access URL: http://arxiv.org/abs/2312.10392
https://zbmath.org/7981229
https://doi.org/10.1137/24m1635879

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.)

File Description: application/xml

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

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

File Description: application/xml

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

On action ground states of defocusing nonlinear Schrödinger equations

Authors: Wei Liu Chushan Wang Xiaofei Zhao

Source: Mathematical Models and Methods in Applied Sciences. 35:39-74

Subject Terms: energy ground state, NLS equations (nonlinear Schrödinger equations), Asymptotic behavior of solutions to PDEs, action ground state, Numerical Analysis (math.NA), Variational principles in infinite-dimensional spaces, Computational methods for problems pertaining to quantum theory, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, rotation, numerical simulations, Mathematics - Analysis of PDEs, 35B38, 35Q55, 58E30, 81-08, asymptotics, Time-dependent Schrödinger equations and Dirac equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, defocusing nonlinear Schrödinger equation, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, quantized vortices, Critical points of functionals in context of PDEs (e.g., energy functionals), Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2311.02890
https://zbmath.org/8005753
https://doi.org/10.1142/s0218202525500022

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

File Description: application/xml

Numerical approximation for stochastic nonlinear fractional diffusion equation driven by rough noise

Authors: Daxin Nie Jing Sun Weihua Deng

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 59:389-418

Subject Terms: Numerical solutions to stochastic differential and integral equations, Smoothness and regularity of solutions to PDEs, finite element method, Fractional processes, including fractional Brownian motion, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, fractional Brownian sheet, Numerical quadrature and cubature formulas, Fractional partial differential equations, 01 natural sciences, Wong-Zakai approximation, Error bounds for initial value and initial-boundary value problems involving PDEs, stochastic fractional diffusion equation, Fractional derivatives and integrals, convolution quadrature, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, PDEs with randomness, stochastic partial differential equations, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, error analysis

File Description: application/xml

Access URL: http://arxiv.org/abs/2201.10897

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

File Description: application/xml

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

A Robust Three-Level Time Split High-Order Leapfrog/Crank-Nicolson Scheme for Two-Dimensional Sobolev and Regularized Long Wave Equations Arising in Fluid Mechanics: A robust three-level time split high-order leapfrog/Crank-Nicolson scheme for two-dimensional Sobolev and regularized long wave equations arising in fluid mechanics

Authors: Ngondiep, Eric

Source: Advances in Applied Mathematics and Mechanics. 17:956-988

Subject Terms: Numerical Analysis (math.NA), three-level time-split high-order leapfrog/Crank-Nicolson approach, stability analysis, 01 natural sciences, leapfrog scheme, Crank-Nicolson method, error estimates, 65M12, 65M06, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Sobolev and regularized long wave equations, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: http://arxiv.org/abs/2211.06298
https://zbmath.org/8033909
https://doi.org/10.4208/aamm.oa-2022-0320

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

File Description: application/xml

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

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

File Description: application/xml

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

Improvements to Enhance Robustness of Third-Order Scale-Independent WENO-Z Schemes: Improvements to enhance robustness of third-order scale-independent WENO-Z schemes

Authors: Li, Qin Yan, Pan Huang, Xiao et al.

Source: Advances in Applied Mathematics and Mechanics. 17:373-406

Subject Terms: Computational Engineering, Finance, and Science (cs.CE), FOS: Computer and information sciences, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, critical point, FOS: Physical sciences, WENO-Z scheme, smoothness indicator, robustness, Computational Physics (physics.comp-ph), Computer Science - Computational Engineering, Finance, and Science, Physics - Computational Physics, 01 natural sciences

File Description: application/xml

Access URL: http://arxiv.org/abs/2208.02343
https://zbmath.org/7976967
https://doi.org/10.4208/aamm.oa-2023-0244

Structure-preserving numerical methods for disease transmission with chemotaxis of singular sensitivity

Authors: Ding, Jie Xu, Ziheng Zhou, Shenggao

Source: Discrete and Continuous Dynamical Systems - B. 30:2684-2708

Subject Terms: Epidemiology, large chemosensitivity, linear stability analysis, pattern dynamics, Finite difference methods for initial value and initial-boundary value problems involving PDEs, positivity preserving, chemotaxis

File Description: application/xml

An Improved WENO-Z+ Scheme: An improved WENO-Z+ scheme

Authors: Li, Ruo Zhong, Wei

Source: Advances in Applied Mathematics and Mechanics. 17:31-68

Subject Terms: WENO scheme, high resolution, Finite difference methods for initial value and initial-boundary value problems involving PDEs, over-amplification, hyperbolic problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml