Numerical methods for systems of nonlinear parabolic equations with time delays
Some numerical aspects of a class of coupled nonlinear parabolic systems with time delays are investigated. The system of parabolic equations is discretized by the finite difference method which yields a coupled system of nonlinear algebraic equations. The mathematical analysis of the nonlinear system is carried out by the method of upper and lower solutions and its associated monotone iterations. Three monotone iterative schemes are presented and it is shown that the sequence of iterations from each one of these iterative schemes converges monotonically to a unique solution of the finite difference system. A theoretical comparison result for the various monotone sequences and error estimates for the three iterative schemes are obtained. It is also shown that the finite difference solution converges to the classical solution of the parabolic system as the mesh size decreases to zero.
scientific article; zbMATH DE number 1398607