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Solving second kind Fredholm integral equations by periodic wavelet Galerkin method. (English) Zbl 1088.65122

Summary: We use the periodized Daubechies wavelets based Galerkin method (PWGM) to solve linear, nonlinear and singular Fredholm integral equations of the second kind. A main advantage of the present PWGM over the existing wavelet Galerkin methods lies in that the wavelet expansion coefficients are exactly obtained without calculating the wavelet integrations. Therefore, the computational cost is low whereas the accuracy is high. After discretization, the linear and nonlinear integral equations is converted into a system of linear and nonlinear equations, respectively, and for the linear case the matrix can be converted into a sparse and symmetrical one by the fast wavelet transform. Numerical experiments show that the PWGM has a good degree of accuracy.

MSC:

65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
65T60 Numerical methods for wavelets
45G10 Other nonlinear integral equations
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