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On the solution of boundary value problems with nonseparated multipoint and integral conditions

Abstract

We suggest a numerical method for solving systems of linear nonautonomous ordinary differential equations with nonseparated multipoint and integral conditions. By using this method, which is based on the operation of convolution of integral conditions into local ones, one can reduce the solution of the original problem to the solution of a Cauchy problem for systems of ordinary differential equations and linear algebraic equations. We establish bounded linear growth of the error of the suggested numerical schemes. Numerical experiments were carried out for specially constructed test problems.

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Original Russian Text © K.R. Aida-zade, V.M. Abdullaev, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 9, pp. 1152–1162.

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Aida-zade, K.R., Abdullaev, V.M. On the solution of boundary value problems with nonseparated multipoint and integral conditions. Diff Equat 49, 1114–1125 (2013). https://doi.org/10.1134/S0012266113090061

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Keywords

  • Cauchy Problem
  • Integral Condition
  • Nonlocal Condition
  • Multipoint Boundary
  • Convolution Function