Numerical solution of a quasilinear parabolic problem

A combined approach of linearisation techniques and finite difference method is presented for obtaining the numerical solution of a quasilinear parabolic problem. The given problem is reduced to a sequence of linear problems by using the Picard or Newton methods. Each problem of this sequence is approximated by Crank-Nicolson difference scheme. The solutions of the resulting system of algebraic equations are obtained by using Block-Gaussian elimination method. Two numerical examples are solved by using both linearisation procedures to illustrate the method. For these examples, the Newton method is found to be more effective, especially when the given nonlinear problem has steep gradients.