An approximation to the solution of time fractional modified Burgers’ equation using extended cubic B-spline method

This paper aims to investigate numerical solution of time fractional modified Burgers’ equation via Caputo fractional derivative. Extended cubic B-spline collocation scheme which reduces the nonlinear equation to a system of linear equation in the matrix form has been used for this investigation. The nonlinear part in fractional partial differential equation has been linearized by modified form of the existing method. The validity of proposed scheme has been examined on three test problems and effect of viscosity ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu $$\end{document} and αϵ[0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \ \epsilon \ [0, 1]$$\end{document} variation displayed in 2D and 3D graphics. Moreover, the working of proposed scheme has also been explained through algorithm and stability of proposed scheme has been analyzed by von Neumann scheme and has proved to be unconditionally stable. To quantify the accuracy of suggested scheme, error norms have been computed.