Quasi-boundary Value Method for Backward Heat Conduction Equation with Variable Coefficients

Abstract

Aiming at the problem of inhomogeneous backward heat conduction equation with time-dependent coefficients in a one- dimensional region , the quasi-boundary value method is used to solve this problem. Firstly , the solution of the problem is obtained by separating variables , and according to the expression of the solution of the problem , the regular solution is constructed; secondly , when the solution of the original problem satisfies some prior conditions , the priori and posteriori methods for the regularization parameter are given respectively , and the convergence of the regularization solution of the problem of one-dimensional backward heat conduction equation under this parameter selection criterion is strictly proved; finally , numerical simulation shows that quasi-boundary value method is effective and stable.