NUMERICAL SOLUTION OF A QUASILINEAR PARABOLIC PROBLEM WITH PERIODIC BOUNDARY CONDITION

In this paper we study the one dimensional mixed problem, with Neumann and Dirichlet type periodic boundary conditions, for the quasilinear parabolic equation (partial)u/(partial)t − a^2* (partial^2)u/(partial)x^2 = f(t, x, u). We construct an iteration algorithm for the numerical solution of this problem. We analyze computationally convergence of the iteration algorithm, as well as on test examples. We demonstrate a numerical procedure for this problem on concrete examples, and also we obtain numerical solution by using the implicit finite difference algorithm