Nonlinear dynamics of the Fisher's equation with numerical experiments

G. Arora; S. Mishra; B.K. Singh

G. Arora Department of Chemical Engineering and Physical Sciences, Lovely Professional University, India.
S. Mishra Department of Chemical Engineering and Physical Sciences, Lovely Professional University, India.
B.K. Singh School of Physical and Decision Sciences, Department of Mathematics, Babasaheb Bhimrao Ambedkar University, India

Abstract

Present work establishes a hybrid approach called as Crank-Nicolson differential quadrature method (DQM) for evaluating the solution of the Fisher’s equation via utilization of modified B-spline as basis functions. The novelty of the proposed scheme is the implementation of DQM on the referred equation after the implementation of Crank–Nicolson scheme. The existing nonlinear terms are re-framed in a linear form via Rubin–Graves approach. The accuracy of the hybrid scheme is presented by the errors obtained in the numerical test problems solved numerically by the approach and hence comparing the solution with already established methods. From the presented comparisons it can be observed that the hybrid approach is providing the solutions for a relatively less number of grid points as compared to the collocation approach and produces comparable results with schemes reported in the literature.