Numerical method for solving nonlinear boundary value problem for differential equations with retarded argument

Mathematica modeling, numerical technique and program complexes


Аuthors

Afanas'eva M. A.*, Kuznetsov E. B.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: mary.mai.8@yandex.ru
**e-mail: kuznetsov@mai.ru

Abstract

Considered the numerical solution of nonlinear boundary value problems for differential equations with delay by the false position method. Affecting the question of finding false position method’s parameter with more accurate methods of finding a number of possible parameter values and find the parameter in the case of solutions of a singularly perturbed equation. For more accurate location solutions and for finding all possible solutions used E. Lanaye’s parameter continuation method and the method of continuation with respect to the best parameter. The numerical studies demonstrate the advantage of using the described approach. In the case of solving a system of singularly perturbed equations using the false position method and the method of optimal parametrization it is possible to find all the solutions with the required accuracy, while other methods are not always possible to find all the solutions. Cauchy problem on each step of the the false position method solved by Runge-Kutta method of fourth order of accuracy. The suggested method of solution differential equation with retarded argument can be useful for solving tasks of mechanics of deformable solids, radiolocation, theory of automatic control.

Keywords:

differential equations with retarded argument, numerical Methods, false position method, method of continuation with respect to the best parameter, E. Lanaye’s parameter continuation method

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