Numerical Computation on Analyticity of the Solution of a Cauchy Problem for the Backward Heat Equation

Abstract

In the paper a simple problem with two parameters for the backward heat equation is proposed. One parameter provides various situations: an initial and boundary value problem, a continuation problem and an initial value problem. Numerical results show that IPNS(Infinite-Precision Numerical Simulation) is superior in the stability rather than the simple discretization method. Numerical results by IPNS suggest existence and non-existence of the solution.