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In this article, a meshless method using the spacetime collocation for solving the two-dimensional backward heat conduction problem (BHCP) is proposed. The spacetime collocation meshless method (SCMM) is to derive the general solutions as the basis functions for the two-dimensional transient heat equation using the separation of variables. Numerical solutions of the heat conduction problem are expressed as a series using the addition theorem. Because the basis functions are the general solutions of the governing equation, the boundary points may be collocated on the spacetime boundary of the domain. The proposed method is verified by conducting several heat conduction problems. We also carry out numerical applications to compare the SCMM with other meshless methods. The results show that the SCMM is accurate and efficient. Furthermore, it is found that the recovered boundary data on inaccessible boundary can be obtained with high accuracy even though the over specified data are provided only at a 1/6 portion of the spacetime boundary.

A Novel Spacetime Collocation Meshless Method for Solving Two-Dimensional Backward Heat Conduction Problems