A numerical-analytical method for constructing self-similar solutions of the heat conduction equation with power-law nonlinearity in the non-blow-up domain

Abstract

In this paper, a self-similar solution of the heat conduction equation with a power-law nonlinear source is considered. The reduced equation is studied using a numerical-analytical method based on a modification of the shooting method. A theorem on the existence and uniqueness of the solution in the neighborhood of the initial conditions is proved, where the solution is sought in the form of a Taylor series. To apply the obtained theoretical results in numerical computations, an estimate of the truncation error of the series remainder was derived, and the problem of analytic continuation of the obtained solution beyond the convergence domain was addressed.