Numerical algorithm for parabolic problems with non-classical conditions

The parabolic problems with non-classical conditions are discussed in a reproducing kernel space in this paper. A reproducing kernel space is constructed, in which the non-classical conditions of the parabolic problems are satisfied. Based on the reproducing kernel space, a new technique for solving the non-classical parabolic problems is presented. Some examples are displayed to demonstrate the validity and applicability of the proposed method.