On a collocation method for the time-fractional convection-diffusion equation with variable coefficients

TL;DR

This paper introduces a novel collocation method combining wavelet operational matrices and exponential spline interpolation to effectively solve variable coefficient time-fractional convection-diffusion equations, demonstrating its accuracy and applicability.

Contribution

It develops a new collocation approach integrating sine-cosine wavelet operational matrices with exponential B-splines for solving complex fractional PDEs with variable coefficients.

Findings

Method accurately solves test problems

Numerical results confirm validity and efficiency

Approach applicable to various fractional PDEs

Abstract

In this work, a new collocation approach using a combination of a wavelet operational matrix method and the exponential spline interpolation is proposed to solve the time-fractional convection-diffusion equation with variable coefficients. The operational matrix of fractional order integration is first derived based on sine-cosine wavelet functions, which helps to convert the underlying equation into a linear algebraic system. Then, an exponential B-spline method is introduced in spatial direction. On selecting a set of proper collocation points, the method in presence is evaluated on several test problems and the numerical results finally illustrate its validity and applicability.