Stability and convergence of difference scheme for nonlinear evolutionary type equations (Q949320)

A finite difference scheme of Crank-Nicolson type is derived for an initial-boundary value problem for a nonlinear system \[ \frac{\partial u}{\partial t} = A \frac{\partial^2 u}{\partial x^2} + f(u) \] in which \(A\) is a matrix with complex entries. Convergence and stability in the sup-norm is proved and numerical experiments are shown to validate the theory developed.