Application of trigonometric B-spline functions for solving Caputo time fractional gas dynamics equation

Abstract

In this study, we present a numerical method that utilizes trigonometric cubic B-spline functions to solve the time fractional gas dynamics equation, which is a key component in the study of physical phenomena such as explosions, combustion, detonation and condensation in a moving flow. The Caputo formula is used to define the fractional time derivative, which generalizes the framework for both singular and non-singular kernels. To discretize the unknown function and its derivatives in the spatial direction, we employ trigonometric cubic B-spline functions, while the usual finite difference formulation is used to approximate the Caputo time fractional derivative. A stability analysis of the scheme is provided to ensure that errors do not propagate over time, and a convergence analysis is conducted to measure the accuracy of the solution. To demonstrate the effectiveness of the proposed methodology, we solve various relevant examples and present graphical and tabular results to evaluate the outcomes of the strategy.

Keywords

• time fractional gas dynamics equation
• trigonometric cubic b-spline functions
• finite difference formulation
• collocation method
• stability
• convergence analysis