Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method

Abstract

Abstract This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L 1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank–Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers’ and Fisher’s equations. The error norms $L_{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> and $L_{\infty }$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>L</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math> have been calculated to validate the efficiency and accuracy of the presented algorithm.