Stability and Numerical Simulation of 2D Fractional Pseudo-Hyperbolic Partial Differential Equations

Abstract

This study investigates the numerical solution and stability analysis of two-dimensional fractional pseudo-hyperbolic partial differential equations. Recent advancements in fractional calculus have demonstrated its efficacy in modelling complex physical phenomena, particularly through generalized derivatives that capture memory and non-local effects. The primary contribution of this work is the development and analysis of finite difference schemes for solving initial boundary value problems associated with two dimensional fractional pseudo-hyperbolic equations. We propose first-order accurate difference schemes that incorporate Caputo fractional derivatives with order 1 . Comprehensive error analysis is conducted through numerical simulations, and Von Neumann stability analysis establishes the conditional stability of the proposed numerical method. Experimental validation confirms the accuracy and reliability of the proposed schemes against exact solutions.