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

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 H ¹ norms. The method presented in this article is found to be of order (∆t ^3- + h ⁴). 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.