Computational error analysis of periodic solutions for singular semilinear parabolic problems

Abstract

By using the monotone method, a theoretical and computational method is given to find, to the degree of accuracy desired, approximate solutions of a class of singular semilinear parabolic problems. So that the error between the actual solution and its approximation is within a given error tolerance, the number of iterations is determined. Since each iterate is in terms of an infinite series, the number of terms to be retained in each iterate is determined so that its error from the exact iterate is within a given error tolerance. An improved rate of convergence is then given to show that it is possible to reduce the number of terms retained in each iterate. An algorithm is also described to obtain numerical solutions. For illustration of the computational methods developed, a numerical example is given.