About an approximate solution to the Fredholm integral equation of the first kind by the residual method
Vitaliy Pavlovich Tanana, Evgeniy Yurevich Vishnyakov, Anna Ivanovna Sidikova
Keywords: регуляризация, метод невязки, модуль непрерывности, оценка погрешности, некорректная задача, regularization, method of residuals, module of continuity, evaluation of inaccuracy, ill-posed problem
Abstract
The Tikhonov finite-dimensional approximation was applied to an integral equation of the first kind. This allowed us to use the variation regularization method of choosing the regularization parameter residuals from the principle of reducing the problem to a system of linear algebraic equations. The estimate of accuracy of the approximate solution with allowance for the error of the finite-dimensional problem approximation has been obtained. The use of this approach is illustrated on an example of solving an inverse boundary value problem for the heat conductivity equation.
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