Bekbosyn A.D.
SOLVING THE CAUCHY PROBLEM BY THE RUNGE-KUTTA METHOD *
Аннотация:
the relevance of the topic is determined by the importance of practical applications of the theory of boundary value problems for differential equations in solving various problems of science and technology, on the one hand, and the need to create new effective methods for solving boundary value problems for differential equations, on the other.
Ключевые слова:
cauchy problem, method Runge-Kutta, Taylor series, parameter The task is given (1) (2) (1), (2) report accuracy of approximate resolution (3) consider the Runge-Kutta method of approximate calculation of this integral, since it is directly related to the accuracy of calculating the integral to the right of its equality
A METHODWWАннотация: the relevance of the topic is determined by the importance of practical applications of the theory of boundary value problems for differential equations in solving various problems of science and technology, on the one hand, and the need to create new effective methods for solving boundary value problems for differential equations, on the other.Ключевые слова: cauchy problem, method Runge-Kutta, Taylor series, parameterThe task is given(1)(2)(1), (2) report accuracy of approximate resolution(3)consider the Runge-Kutta method of approximate calculation of this integral, since it is directly related to the accuracy of calculating the integral to the right of its equality.TT To do this, first enter the variable let's convert:, (4)here. Now(5)to calculate the integralselect parameters, , using the parametersstep-by-step calculation of the circuit,(6)the approximation is as follows, , let's look at how to find parameters.Let's say,(7)let it be. assuming it is a sufficiently horizontal function, let's classify it as:Now, , parameters(8)if we find it in such a way that it happens, then the mistake we make:(9)It is classified by the degree of h by comparison with the expression, the unknowns of, , we obtain a system of nonlinear equations consisting of parameters. By solving this system of equations, , we find the parameters.For any, , since finding the parameters is a difficult task, we will consider only independent cases of this method.When solving the problem (2), (3) by the Runge-Kutta method, four numbers are determined as follows:if we say, then can be shown.
Номер журнала Вестник науки №6 (75) том 1
Ссылка для цитирования:
Bekbosyn A.D. SOLVING THE CAUCHY PROBLEM BY THE RUNGE-KUTTA METHOD // Вестник науки №6 (75) том 1. С. 1895 - 1898. 2024 г. ISSN 2712-8849 // Электронный ресурс: https://www.вестник-науки.рф/article/15423 (дата обращения: 23.05.2025 г.)
Вестник науки © 2024. 16+