Numerical solution of backward heat conduction problems by a high order lattice‐free finite difference method

Abstract

We construct a high order finite difference method in which quadrature points do not need to have a lattice structure. In order to develop our method we show two tools using Fourier transform and Taylor expansion, respectively. On the other hand, the backward heat conduction problem is a typical example of ill‐posed problems in the sense that the solution is unstable for errors of data. Our aim is creation of a meshless method which can be applied to the ill‐posed problem. From numerical experiments we confirmed that our method is effective in solving two‐dimensional backward heat conduction equations subject to the Dirichlet boundary condition.