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

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.

Keywords

• Fractional calculus
• Wavelet methods
• Numerical simulations
• Burgers’ equation
• Fisher–KPP equation
• Nonlinear Schrödinger equation