Orthogonal cubic spline collocation method for the extended Fisher–Kolmogorov equation

A second-order splitting combined with orthogonal cubic spline collocation method is formulated and analysed for the extended Fisher–Kolmogorov equation. With the help of Lyapunov functional, a bound in maximum norm is derived for the semidiscrete solution. Optimal error estimates are established for the semidiscrete case. Finally, using the monomial basis functions we present the numerical results in which the integration in time is performed using RADAU 5 software library.