Approximate solution of first kind singular integral equation with generalized kernel using Legendre multiwavelets. (English) Zbl 1438.65339
Summary: In this study, numerical solution of a class of Cauchy type singular integral equations of the first kind with generalized kernels (CSIEFKGK) is obtained using Legendre multiwavelets (LMW). Instead of using complex function theory, the appropriate weight function of the solution is obtained by applying LMW-based numerical scheme. We evaluate the matrix representation of generalized kernel with and without the weight factor using recurrence relations and some elementary methods. Using the multiscale representation of the integral operator, the equation is converted into a system of linear equations. The numerical solution of CSIEFKGK is obtained by solving this systems. Finally, a number of examples including applications of crack problems are considered to illustrate the efficiency of the method developed here.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45E05 | Integral equations with kernels of Cauchy type |
| 65D15 | Algorithms for approximation of functions |
| 65T60 | Numerical methods for wavelets |
Keywords:
Cauchy type singular integral equation of the first kind; generalized kernel; Legendre multiwavelets; wavelet Galerkin method; multiscale approximationSoftware:
DLMFReferences:
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