A new spline technique for the time fractional diffusion-wave equation

Abstract

The current research article proposes an approximate solution of the fractional diffusion wave equation (FDWE) by using a new collocation method based on the cubic B-splines. The fractional derivative in the time direction is considered in Caputo form. The theoretical research of the proposed algorithm is discussed with L∞ and H1 norms. The method presented in this article is found to be of order (∆t3−α + h4). The highlights of the current technique proposed in this article are as under: • The method is high-order collocation and uses a compact stencil. The error analysis is discussed to authenticate the order of convergence of the proposed numerical approximation. • The comparisons of errors with the already existing methods are done and observed that our method produces more accurate results than the methods presented in the literature.

Keywords

• Spline Collocation Method