Xiaojing Liu1, Jizeng Wang1,2, Youhe Zhou1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.5, pp. 493-505, 2013, DOI:10.3970/cmes.2013.092.493
Abstract By combining techniques of boundary extension and Coiflet-type wavelet expansion, an approximation scheme for a function defined on a two-dimensional bounded space is proposed. In this wavelet approximation, each expansion coefficient can be directly obtained by a single-point sampling of the function. And the boundary values and derivatives of the bounded function can be embedded in the modified wavelet basis. Based on this approximation scheme, a modified wavelet Galerkin method is developed for solving two-dimensional nonlinear boundary value problems, in which the interpolating property makes the solution of such strong nonlinear problems very effective and accurate. As an example, we… More >
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