An Efficient Numerical Technique for Solving Time-Fractional Generalized Fisher's Equation - Majeed, Abdul; Kamran, Mohsin; Abbas, Muhammad; Singh, Jagdev (Frontiers in Physics, 2020)
This paper extends the existing Fisher equation by adding the source term and generalizing the degree $β$ of non-linear part. Numerical solutions of modified Fisher's equation for different values of $β$ using cubic B-spline collocation scheme are investigated. The fractional derivative in time dimension is discretized in Caputo's form based on $L1$ formula, while cubic B-spline basis functions are used to interpolate the spatial derivative. The non-linear part in the equation is linearized by the modified formula. The efficiency of the proposed scheme is examined by considering four test examples with different initial and boundary conditions. The effect of different parameters is discussed and presented in the form of tables and graphics. Moreover, by Von Neumann stability formula, proposed scheme is shown to be unconditionally stable. The results of error norms reflect that present scheme is suitable for non-linear time fractional differential equations.