Geodesic
Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 7, pp. 1096-1109 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical method is suggested for solving systems of nonautonomous loaded linear ordinary differential equations with nonseparated multipoint and integral conditions. The method is based on the convolution of integral conditions into local ones. As a result, the original problem is reduced to an initial value (Cauchy) problem for systems of ordinary differential equations and linear algebraic equations. The approach proposed is used in combination with the linearization method to solve systems of loaded nonlinear ordinary differential equations with nonlocal conditions. An example of a loaded parabolic equation with nonlocal initial and boundary conditions is used to show that the approach can be applied to partial differential equations. Numerous numerical experiments on test problems were performed with the use of the numerical formulas and schemes proposed. 
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V. M. Abdullaev; K. R. Aida-zade. Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 7, pp. 1096-1109. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_7_a2/

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