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Well-posedness and uniform approximations of the solution of a boundary value problem for a singular integro-differential equation. (English) Zbl 1457.65251

Summary: On a real segment, we consider a boundary value problem for a singular integro-differential equation of the first kind with the Cauchy kernel in the characteristic part. The well-posedness of this problem, established by the authors on a pair of specially selected spaces, allows to use approximate methods for its solving. We propose a general projection method, establish the conditions for its convergence in the chosen spaces and estimates the error of approximate solutions. As a result, uniform error estimates are obtained. A computational scheme of the wavelet collocation method is constructed, its theoretical substantiation is carried out, the results of a numerical experiment are presented on a model example.

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
65T60 Numerical methods for wavelets
47G20 Integro-differential operators
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