Convergence analysis for an iterative method for solving nonlinear parabolic systems

In a recent work, we have proposed a new iterative method based on the eigenfunction expansion to integrate nonlinear parabolic systems sequentially. In this paper, we prove that the method is convergent and give analytical rate for its convergence. Moreover, we determine the number of iterations needed to obtain a solution with a pre-determined level of accuracy. We then illustrate the convergence analysis with a problem in combustion theory. It is expected that the convergence analysis can be used for similar systems with time dependence.