Computational methods for time-periodic solutions of singular semilinear parabolic problems

Abstract

Existence and uniqueness of time-periodic solutions for a class of singular semilinear parabolic problems are established by the method of alternating bounds and the Picard method respectively. For each method, the number of iterations and the number of terms retained in each successive iterate (which is in terms of an infinite series) are determined such that the difference between the resulting approximation and the actual solution is within the degree of accuracy desired. Under additional assumptions, it is shown that the rates of convergence can be improved so that the number of terms retained in each iterate may be reduced without sacrificing accuracy.