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Some iterative processes of solution of elliptic equations with discontinuous coefficients and solutions with a design estimates of the rate of convergence of iterations

F. V. Lubyshev1, M. E. Fairuzov2

AnnotationWe study the approximate solution of the contact boundary problems for elliptic equations in inhomogeneous anisotropic media with discontinuous coefficients and solution when contacting the internal borders of multilayer media define the conditions of conjugation nonideal contact type. Developed and validated method for solving these classes of problems with discontinuous coefficients and solutions to equations of mathematical physics of elliptic type. Questions of convergence of the iterative process. And the set design of the rate of convergence of iterations (with calculated constants).
Keywordsiteration method, mathematical modeling, elliptic equation, problems for equations of mathematical physics with discontinuous coefficients and solutions, the operator.

1full professor of Bashkir State University, Department of Applied Computer Science and Numerical Methods; fairuzovme@mail.ru.

2associate professor of Bashkir State University, Department of Applied Computer Science and Numerical Methods; fairuzovme@mail.ru.

Citation: F. V. Lubyshev, M. E. Fairuzov, "[Some iterative processes of solution of elliptic equations with discontinuous coefficients and solutions with a design estimates of the rate of convergence of iterations]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,16:1 (2014) 89–107 (In Russian)