A Finite Difference Scheme based on Cubic Trigonometric B-splines for Time Fractional Diffusion-wave Equation
Provides an efficient numerical method for solving fractional diffusion-wave equations, relevant to researchers in computational mathematics and physics.
The paper proposes a numerical scheme for solving the time fractional diffusion-wave equation using cubic trigonometric B-splines, achieving superior accuracy and lower computational cost compared to Hermite formula and radial basis function methods.
In this paper, we propose an efficient numerical scheme for the approximate solution of the time fractional diffusion-wave equation with reaction term based on cubic trigonometric basis functions. The time fractional derivative is approximated by the usual finite difference formulation and the derivative in space is discretized using cubic trigonometric B-spline functions. A stability analysis of the scheme is conducted to confirm that the scheme does not amplify errors. Computational experiments are also performed to further establish the accuracy and validity of the proposed scheme. The results obtained are compared with a finite difference schemes based on the Hermite formula and radial basis functions. It is found that our numerical approach performs superior to the existing methods due to its simple implementation, straight forward interpolation and very less computational cost.