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arXiv · 1611.10243

Accurate method of verified computing for solutions of semilinear heat equations

Akitoshi Takayasu·Makoto Mizuguchi·Takayuki Kubo·Shin'ichi Oishi
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Abstract

We provide an accurate verification method for solutions of heat equations with a superlinear nonlinearity. The verification method numerically proves the existence and local uniqueness of the exact solution in a neighborhood of a numerically computed approximate solution. Our method is based on a fixed-point formulation using the evolution operator, an iterative numerical verification scheme to extend a time interval in which the validity of the solution can be verified, and rearranged error estimates for avoiding the propagation of an overestimate. As a result, compared with the previous verification method using the analytic semigroup, our method can enclose the solution for a longer time. Some numerical examples are presented to illustrate the efficiency of our verification method.

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Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi. 2016-11-30. Accurate method of verified computing for solutions of semilinear heat equations. https://arxiv.org/abs/1611.10243

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