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

Adel R. Hadhoud, Faisal E. Abd Alaal, Ayman A. Abdelaziz, Taha Radwan
2021 Demonstratio Mathematica  
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
more » ... roposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.
doi:10.1515/dema-2021-0040 fatcat:wattcevxejbhdlym25qg7e7e3i