An RBF-PUM finite difference scheme for forward-backward heat equation. (English) Zbl 1524.65648
Summary: In this paper, a truly meshless method based on the partition of unity method (PUM) is developed for the numerical solution of the two-dimensional forward-backward heat equations. We propose a novel method according to the domain decomposition scheme and RBF-PUM technique. Particularly, the physical domain needs to be separated into two subdomains each defining a forward or a backward subproblem. The subproblems have been treated by a radial basis function meshfree method based on partition of unity for spatial dimension and a finite difference scheme for the time derivative. In addition, we prove that the time discrete scheme is stable and convergent. Some numerical experiments are going to be presented to show the performance of the proposed method.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 65Y20 | Complexity and performance of numerical algorithms |
| 35K05 | Heat equation |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65D12 | Numerical radial basis function approximation |
Keywords:
forward-backward heat problem; meshless methods; RBF collocation method; partition of unityReferences:
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