Computer-Aided Geometric Design

Numerical solution of hyperbolic telegraph equation by cubic B-spline collocation method

A computational approach based on finite difference scheme and a redefined extended B-spline functions is presented to study the approximate solution of time fractional advection diffusion equation. The Caputo time-fractional derivative and redefined extended B-spline functions have been used for the time and spatial discretization, respectively. The numerical scheme is shown to be O ( h 2 + Δ t 2 - α ) accurate and unconditionally stable. The proposed method is tested through some numerical experiments involving homogeneous/non-homogeneous boundary conditions which concluded that it is more accurate than existing methods. The simulation results show superior agreement with the exact solution as compared to existing methods.

A computational approach for solving time fractional differential equation via spline functions

In this paper, a new method “extended modified cubic B-spline differential quadrature method (EMCB-DQM)” is introduced by using extended modified cubic B-spline functions as test functions in the traditional differential quadrature method. The accuracy and efficiency of the method are tested in view of three numerical problems. The obtained results are compared with the exact solutions and with the results available in the literature. The simple algorithm, least computational efforts and good accuracy are the main advantages of the proposed method. Thus, the proposed method may be used as an alternative method for the numerical treatment of the nonlinear partial differential equations (PDEs). The stability analysis of the method is also carried out.

https://cyberleninka.org/article/n/684367.pdf

Extended modified cubic B-spline algorithm for nonlinear Fisher’s reaction-diffusion equation

The collocation method based on the extended B-spline functions as trial functions is set up to find numerical solutions of the advection-diffusion equation numerically. The transport of the pollution is simulated by way of using solutions of the advection-diffusion equation. Comparative results of use of both B-spline and extended B-spline in the collocation method are illustrated. It is concluded that a suitable selection of the free parameter of extended B-spline is shown to provide less error for the numerical solutions of the advection-diffusion equation with some boundary and initial conditions.

Guo-Zhao Wang

Papers

Extended Cubic Uniform B-spline and α-B-spline