A simple algorithm for solving Cauchy problem of nonlinear heat equation without initial value

Abstract

We develop a novel yet simple non-iterative algorithm to solve Cauchy problem of nonlinear sideways heat equation without initial value. First, we transform the nonlinear heat conduction equation into a new one, including a spring term and a damping term, which can raise the accuracy of numerical solution. Then, we apply a two-stage group-preserving scheme to integrate the semi-discretized equations. Although under a large random noise, the accuracy and stability of the new method are assured from numerical tests.