Approximate solution of time-fractional gas dynamics equation using exponential B-spline functions

Abstract

The current study investigates a numerical method based on exponential cubic B-spline functions to examine the approximate solution of a nonlinear time-fractional gas dynamics equation. The suggested technique employs the usual finite-difference formulation to approximate the Caputo fractional time derivative and exponential B-spline basis functions to interpolate the solution curve along the spatial direction. Stability analysis is provided to ensure that the error does not amplify during the computational process. The uniform convergence of the suggested approach is also discussed. The effectiveness and accuracy of the proposed method are tested through numerical simulations. Graphical and tabular results are exhibited to evaluate the outcomes of the proposed strategy. The major advantage of the suggested scheme is that the algorithm is straightforward to carry out.