A study of quintic B-spline based differential quadrature method for a class of semi-linear Fisher-Kolmogorov equations

In the present manuscript, Fisher-Kolmogorov equation is solved numerically by adopting a differential quadrature technique that uses quintic B-spline as the basis functions for space integration. The derivatives are approximated using differential quadrature method. The weighting coefficients are obtained by semi-explicit algorithm. Five-band Thomas algorithm has been employed to solve the resultant algebraic system that can be reduced into a penta-diagonal matrix. Stability analysis of method has also been done. The accuracy of the proposed scheme is demonstrated by applying on three test problems. Theoretical attributes such as existence, uniqueness and regularity of Fisher-Kolmogorov equations are also conferred. The outcomes are depicted graphically to confirm accuracy of the findings and performance of this method and a comparative study is done with results available in the literature. The computed results are found to be in good agreement with the analytical solutions.