New solutions of fractional-order Burger-Huxley equation - İnç, Mustafa; Partohaghighi, Mohammad; Akinlar, Mehmet Ali; Agarwal, Paraveen; Chu, Yu-Ming (Elsevier, 2020)
A simple and powerful numerical method is proposed for solving the time-fractional Burger-Huxley equation (TFBH) equation within Caputo type fractional derivative. A fictitious coordinate theta is applied into the equation in order to convert the dependent variable u(x, t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of the method of line and group preserving scheme (GPS) is introduced to find the approximate solutions. The reliability and accuracy of this scheme has been shown through some examples of the TFBH equation.
Keywords: Burger-Huxley equation; Group preserving; Caputo derivative; Fictitious time integration