PofoliaShared via Pofolia

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik· 2026Q2

An Effective Numerical Simulation Algorithm for the Time‐Space Fractional Reaction–Diffusion–Wave Equation With ψ‐Caputo and Riesz Derivatives

Min Cai, Ziyi Chen, Changpin Li

Short summary

A new numerical algorithm effectively simulates the time-space fractional reaction-diffusion-wave equation using the H2N2 formula for ψ-Caputo derivatives and finite element methods for spatial discretization.

AI-generated from the title and abstract; the full text is not read.

Key points

  • Developed a numerical algorithm for time-space fractional reaction-diffusion-wave equations.
  • Employs the H2N2 formula for approximating ψ-Caputo temporal derivatives.
  • Utilizes the finite element method for spatial discretization.
  • Rigorously proved the numerical stability and convergence of the fully discrete scheme.

AI-generated from the title and abstract; the full text is not read.

Abstract

ABSTRACT This paper constructs an effective numerical simulation algorithm for the time‐space fractional reaction–diffusion–wave equation, where the temporal derivative is in the sense of ‐Caputo and the spatial derivative in the sense of Riesz. The H2N2 formula is applied to approximating the ‐Caputo derivative in time and the finite element method is utilized for the spatial discretization. Numerical stability and convergence of the proposed fully discrete scheme are rigorously proved. Numerical implementation for the proposed simulation algorithm is shown in more detail. And the numerical examples are presented to support the theoretical analysis.

The authors' abstract, as published at the source. ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2026 · DOI ↗

TakeawaysPremium
Ask the paperFree account

Continue with a free account

Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.

Continue free on the web

Sign in with Google or Apple; no card needed. You come back to this paper.

On your phone:

Get it on Google Play Download on the App Store

Field: Modeling and Simulation

Modeling and SimulationMathematics