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.