An Efficient Computational Technique based on Cubic Trigonometric B-splines for Time Fractional Burgers' Equation

TL;DR

This paper introduces an efficient linear computational method using cubic trigonometric B-splines for solving the time fractional Burgers' equation, demonstrating high accuracy and stability through theoretical analysis and numerical experiments.

Contribution

The paper develops a novel linearization technique and applies cubic trigonometric B-splines to discretize the spatial derivatives, reducing computational cost and improving accuracy for fractional PDEs.

Findings

Method is unconditionally stable

Numerical results show high accuracy

Compared scheme outperforms parametric spline method

Abstract

This paper presents a linear computational technique based on cubic trigonometric cubic B-splines for time fractional burgers' equation. The nonlinear advection term is approximated by a new linearization technique which is very efficient and significantly reduces the computational cost. The usual finite difference formulation is used to approximate the Caputo time fractional derivative while the derivative in space is discretized using cubic trigonometric B-spline functions. The method is proved to be globally unconditionally stable. To measure the accuracy of the solution, a convergence analysis is also provided. A convergence analysis is Computational experiments are performed to further establish the accuracy and stability of the method. Numerical results are compared with those obtained by a scheme based on parametric spline functions. The comparison reveal that the proposed scheme is quite accurate and effective.