On a problem for a delay differential equation
Iskakova N. Temesheva S. Uteshova R.
June 2023John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2023#46Issue 911283 - 11297 pp.
The article considers a nonlinear boundary value problem for a linear delay differential equation. To solve the problem, the idea of parametrization method, namely, the interval at which the problem is being considered, is divided into subintervals whose lengths do not exceed the values of the constant delay; constant parameters are introduced at the left ends of these intervals; a new unknown function is introduced at each subinterval. Thus, the problem under consideration is reduced to an equivalent multipoint boundary value problem for differential equations with delay containing parameters. Auxiliary Cauchy problems without delay with zero initial conditions at the left ends of the subintervals are consistently considered on each of the subintervals. Using an analog of the Cauchy formula to represent the solution of a system of linear differential equations on each of the subintervals and given nonlinear boundary conditions, an algebraic system with respect to unknown parameters is obtained. The article proposes an algorithm for finding a solution to a multipoint boundary value problem for differential equations with a delay containing parameters. At each step of the algorithm, a system of nonlinear algebraic equations is solved to determine the values of the parameters, and an analog of the Cauchy formula is used to obtain solutions to auxiliary Cauchy problems. The results obtained are demonstrated on a test problem.
algorithm , delay differential equation , isolated solution , nonlinear boundary-value problem
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Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics and Mathematical Modeling, Abai Kazakh National Pedagogical University, Almaty, Kazakhstan
Department of Mathematics, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mathematical and Computer Modeling, International IT University, Almaty, Kazakhstan
Department of Differential Equations
Department of Mathematics and Mathematical Modeling
Department of Mathematics
Department of Mathematical and Computer Modeling
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