On the solvability of a semi-periodic boundary value problem for the nonlinear Goursat equation
Сызықтық емес Гурс теңдеуi үшiн жартылайпериодтық шеттiк есептiң шешiмдiлiгi туралы
О разрешимости полупериодической краевой задачи для нелинейного уравнения Гурса
Orumbayeva N.T. Tokmagambetova T.D. Nurgalieva Zh.N.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#104Issue 4110 - 117 pp.
In this paper, by means of a change of variables, a nonlinear semi-periodic boundary value problem for the Goursat equation is reduced to a linear gravity problem for hyperbolic equations. Reintroducing a new function, the obtained problem is reduced to a family of boundary value problems for ordinary differential equations and functional relations. When solving a family of boundary value problems for ordinary differential equations, the parameterization method is used. The application of this approach made it possible to establish the coefficients of the unique solvability of the semi-periodic problem for the Goursat equation and to propose constructive algorithms for finding an approximate solution.
algorithm , approximate solution , boundary value problem , Goursat equation , second order boundary value problem , semi-periodic boundary value problem
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Karagandy University of the name of academician E.A. Buketov, Karaganda, Kazakhstan
Karagandy University of the name of academician E.A. Buketov
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