Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination

Abstract

In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.

Keywords

• the generalized time-fractional huxley-burgers’ equation
• the mean value theorem
• the cubic b-spline
• collocation method
• stability analysis
• 34dxx
• 35r11
• 65-xx
• 65d07
• 65l60