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Abstract

In the article an approximate solution of linear boundary value problems of second order with variable coefficients in nonstandard region is considered. A condition which improves the rate of convergence approximate solution to the exact solution of the original problem is obtained. Boundary value problem is reduced to minimization of the functional by using the embedding theorem and the theorem on the continuation of the solution. The proposed methodology of solution contributes to the further development of the applications of the new variation method to computational mathematics.