Výsledky vyhledávání - "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

Autoři: Yuxin Zhang Hengfei Ding

Zdroj: Applied Numerical Mathematics. 213:88-107

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Philipp Öffner Louis Petri Davide Torlo

Zdroj: Applied Numerical Mathematics. 212:110-134

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Haifeng Wang Yan Wang Hong Zhang a další

Zdroj: Applied Numerical Mathematics. 212:60-76

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

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

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Valentino C. Pagano G. Conte D. a další

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Bangti Jin Qingle Lin Zhi Zhou

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

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

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Jiachuan Cao Buyang Li Yanping Lin a další

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Regazzoni, Francesco

Zdroj: Numerische Mathematik. 157:249-306

Témata: 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.)

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Weizhu Bao Yifei Li

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2401.13274

On action ground states of defocusing nonlinear Schrödinger equations

Autoři: Wei Liu Chushan Wang Xiaofei Zhao

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

Témata: 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)

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Yuan, Yirang Li, Changfeng Song, Huailing

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

Témata: 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

Popis souboru: application/xml

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

Autoři: Daxin Nie Jing Sun Weihua Deng

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2201.10897

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

Autoři: Srati, Mohammed Oulmelk, Abdessamad Afraites, Lekbir a další

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Ngondiep, Eric

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Li, Jia-Le Don, Wai-Sun Wang, Cai-Feng a další

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Chai, Longtao Wu, Lifei Yang, Xiaozhong

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Li, Qin Yan, Pan Huang, Xiao a další

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Ding, Jie Xu, Ziheng Zhou, Shenggao

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

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

Popis souboru: application/xml

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

Autoři: Li, Ruo Zhong, Wei

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

Témata: 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

Popis souboru: application/xml