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- Title
Determination of the Unknown Boundary Conditions of the Laplace Equation via Regularization B-spline Wavelet approach.
- Authors
Xinming Zhang; Kaiqi Wang
- Abstract
The unknown boundary condition identification problems of the 2-D Laplace equation are considered in this paper. Based on the good characteristics of the B-spline wavelet and Tikhonov regularization method (TRM), a new regularization B-spline wavelet method (RBPWM) is proposed. The novel algorithm could be regarded as one kind of wavelet mesh-free, non-iterative numerical scheme that converts the boundary condition identification problem into a large-scale algebraic equation system that can be solved in a single step. However, the coefficient matrix of the algebraic equation system is ill-conditioned, which will lead to an unstable solution for the case of higher-level noise. The Tikhonov regularization method (TRM) is used to achieve a steady numerical solution to this problem. The current work of this paper has studied four examples with different simulated noise levels for different boundary conditions. The efficiency and accuracy of the presented algorithm are verified with the numerical simulation.
- Subjects
TIKHONOV regularization; ALGEBRAIC equations; EQUATIONS; WAVELET transforms; COMPUTER simulation
- Publication
IAENG International Journal of Applied Mathematics, 2023, Vol 53, Issue 3, p785
- ISSN
1992-9978
- Publication type
Article