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A reliable treatment of Abel’s second kind singular integral equations. (English) Zbl 1253.65202

Summary: The central idea of this paper is to construct a new mechanism for the solution of Abel’s type singular integral equations that is to say the two-step Laplace decomposition algorithm. The two-step Laplace decomposition algorithm is an innovative adjustment in the Laplace decomposition algorithm and makes the calculation much simpler. In this piece of writing, we merge the Laplace transform and decomposition method and present a novel move toward solving Abel’s singular integral equations.

MSC:

65R20 Numerical methods for integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
44A10 Laplace transform
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References:

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