Shannon wavelet method for solving heat conduction problems. (English) Zbl 1202.65158
Summary: We use the Shannon scale basis function to construct a numerical method for solving two-dimensional heat conduction problems. The proposed method is introduced to describe the heat conduction equations, which leads to sparse matrices. The accuracy of the method is demonstrated by a test problem. The numerical result found is in good agreement with the exact solution.
MSC:
65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
65T60 | Numerical methods for wavelets |
65F50 | Computational methods for sparse matrices |