Numerical method for backward heat conduction problems using an arbitrary-order finite difference method

Abstract

This chapter constructs an arbitrarily-high order finite difference schemes to solve a backward heat conduction problem. The backward heat conduction problem is sensitive to errors of data. The aim is to make discretization error arbitrarily small. An algorithm is shown to construct an arbitrary order finite difference schemes. Finite difference schemes are applied to backward heat conduction problems. From numerical examples it is concluded that the arbitrary order difference scheme is effective for solving the 1D backward heat conduction problem under the dirichlet boundary condition.