A hybrid Haar wavelet collocation method for nonlocal hyperbolic partial differential equations

TL;DR

This paper introduces a hybrid numerical method combining Haar wavelets and finite differences to effectively solve nonlocal hyperbolic PDEs with integral boundary conditions, demonstrating improved accuracy and stability.

Contribution

A novel hybrid collocation method utilizing Haar wavelets and finite differences for nonlocal hyperbolic PDEs, efficiently handling integral boundary conditions with proven stability and convergence.

Findings

Numerical results outperform existing methods.

Method is stable and convergent.

Efficient handling of nonlocal boundary conditions.

Abstract

In this paper, we propose a hybrid collocation method based on finite difference and Haar wavelets to solve nonlocal hyperbolic partial differential equations. Developing an efficient and accurate numerical method to solve such problem is a difficult task due to the presence of nonlocal boundary condition. The speciality of the proposed method is to handle integral boundary condition efficiently using the given data. Due to various attractive properties of Haar wavelets such as closed form expression, compact support and orthonormality, Haar wavelets are efficiently used for spatial discretization and second order finite difference is used for temporal discretization. Stability and error estimates have been investigated in order to ensure the convergence of the method. Finally, numerical results are compared with few existing results and it is shown that numerical results obtained by the proposed method is better than few existing results.