| Abstrakt: |
Computation schemes for an approximate solution of a singular integral equation of the first kind bounded at one end and unbounded at the other end of the integration interval are constructed. A solution of the equation is sought for in the form of a series in Chebyshev polynomials of the third and the fourth kinds. The kernel and the right-hand side of the equation are expanded into series with Chebyshev polynomials of the third and the fourth kinds whose coefficients are approximately calculated by Gaussian quadrature formulas, that is, with the highest algebraic order of accuracy. For the coefficients of expansion of the Chebyshev polynomials, exact values in the series are found. The expansion coefficients of the unknown function, that is, the equation solutions, are found by solving systems of linear algebraic equations. To justify the thus constructed computational schemes, some methods of functional analysis and the theory of orthogonal polynomials are used. Under some conditions of existence for given functions of derivatives up to some order belonging to the Hölder class, the calculation error is estimated and the order of its convergence to zero is given. [ABSTRACT FROM AUTHOR] |
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