A finite difference scheme based on cubic trigonometric B-splines for a time fractional diffusion-wave equation

Abstract

In this paper, we propose an efficient numerical scheme for the approximate solution of a 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 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, straightforward interpolation and very low computational cost. A convergence analysis of the scheme is also discussed.

Crank-Nicolson orthogonal spline collocation method combined with WSGI difference scheme for the two-dimensional time-fractional diffusion-wave equation

“…Generally, the analytical solutions of fractional partial di erential equations are di cult to obtain, so many authors have resorted to numerical solution techniques based on convergence and stability. Various kinds of numerical methods for solving FPDEs have been proposed by researchers, such as nite element method [2,3], nite di erence method [4][5][6], meshless method [7,8], wavelets method [9],spline collocation method [10][11][12] and so forth.…”

A fully implicit finite difference scheme based on extended cubic B-splines for time fractional advection–diffusion equation

“…Zhu and Nie [23] obtained a scheme based on exponential B-spline and wavelet operational matrix method for the time fractional convection-diffusion problem with variable coefficients. Yaseen et al [24] constructed a finite difference method for solving time fractional diffusion problem via trigonometric B-spline. Zhu et al [25] derived an efficient differential quadrature scheme based on modified trigonometric cubic B-spline for the solution of 1D and 2D time fractional advection-diffusion equations.…”

Numerical Solution of Fractional Diffusion Wave Equation and Fractional Klein–Gordon Equation via Two-Dimensional Genocchi Polynomials with a Ritz–Galerkin Method

“…Moreover, second order finite difference schemes were recommended for the solution of the time-fractional diffusion wave equation in [7]. A finite difference scheme based on cubic trigonometric B splines was derived by [8] to solve the FDWE.…”