Cubic B-spline collocation method for solving time fractional gas dynamics equation

Abstract

In the present manuscript, a cubic B-spline finite element collocation method has been used to obtain numerical solutions of the nonlinear time fractional gas dynamics equation. While the Caputo form is used for the time fractional derivative appearing in the equation, the $L1$ discretization formula is applied to the equation in terms of time. It has been seen that the results of the present study are in agreement with the those of exact solution. Therefore, the present method can be used as an alternative and efficient one to find out the numerical solutions of both linear and nonlinear fractional differential equations available in the literature. In order to control the accuracy and efficiency of the present method, the error norms $L_{2}$ and $L_{\infty}$ have been calculated. It is evident that the newly obtained numerical solutions by the present method can be computed easily with the implementation and effectiveness of the approach used in the article.