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A method of solving a nonlinear boundary value problem with a parameter for a loaded differential equation
Authors:Dulat Dzhumabaev  Elmira Bakirova  Sandugash Mynbayeva
Affiliation:Institute of Mathematics and Mathematical Modeling, 125, Pushkin Str., Almaty, 050010 Kazakhstan
Abstract:A nonlinear loaded differential equation with a parameter on a finite interval is studied. The interval is partitioned by the load points, at which the values of the solution to the equation are set as additional parameters. A nonlinear boundary value problem for the considered equation is reduced to a nonlinear multipoint boundary value problem for the system of nonlinear ordinary differential equations with parameters. For fixed parameters, we obtain the Cauchy problems for ordinary differential equations on the subintervals. Substituting the values of the solutions to these problems into the boundary condition and continuity conditions at the partition points, we compose a system of nonlinear algebraic equations in parameters. A method of solving the boundary value problem with a parameter is proposed. The method is based on finding the solution to the system of nonlinear algebraic equations composed.
Keywords:loaded differential equation with parameter  method of solving  nonlinear boundary value problem
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