Computational precision in time fractional PDEs: Euler wavelets and novel numerical techniques

Document Type

Article

Source of Publication

Partial Differential Equations in Applied Mathematics

Publication Date

12-1-2024

Abstract

This paper presents innovative numerical methodologies designed to solve challenging time fractional partial differential equations, with a focus on the Burgers’, Fisher–KPP, and nonlinear Schrödinger equations. By employing advanced wavelet techniques integrated with fractional calculus, we achieve highly accurate solutions, surpassing conventional methods with minimal absolute error in numerical simulations. A thorough series of numerical experiments validates the robustness and effectiveness of our approach across various parameter regimes and initial conditions. The results underscore significant advancements in the computational modeling of complex physical phenomena governed by time fractional dynamics and offering a powerful tool for a wide range of applications in science and engineering.

ISSN

2666-8181

Publisher

Elsevier BV

Volume

12

First Page

100918

Last Page

100918

Disciplines

Mathematics

Keywords

Fractional calculus, Wavelet techniques, Partial differential equations, Numerical simulations, Robustness

Indexed in Scopus

no

Open Access

no

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