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.
@article{arxiv.1604.02112,
title = {On a collocation method for the time-fractional convection-diffusion equation with variable coefficients},
author = {Xiaogang Zhu and Yufeng Nie},
journal= {arXiv preprint arXiv:1604.02112},
year = {2016}
}