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- W3210361459 abstract "Periodical boundary value problem for the Van der Pol differential equation is solved by parametrization’s method. Interval is divided into 2 parts, the values of the solution at the left-end points of the subintervals are considered as additional parameters and original problem is reduced to the boundary value problem with parameters. Using solutions to the Cauchy problems for the differential equations with parameters, boundary condition, and the continuity condition at the dividing point, a system of nonlinear algebraic equations with respect to introduced parameters is composed. Explicit form of this system exists in exceptional cases. However, for the given parameters, the values of functions, which present left-hand sides of the system, and their derivatives by parameters, we can find by solving the Cauchy problems for ordinary differential equations on the subintervals. We find solutions to the Cauchy problems by forth order Runge-Kutta method. The solution of the composed system is found by Newton’s method." @default.
- W3210361459 created "2021-11-08" @default.
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- W3210361459 date "2019-05-31" @default.
- W3210361459 modified "2023-09-27" @default.
- W3210361459 title "An algorithm of solving nonlinear boundary value problem for the Van der Pol differential equation: Dzhumabaev D.S., Mursaliyev D.E., Sergazina A.S., Kenjeyeva A.A." @default.
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