Well-posedness of a periodic boundary value problem for the system of hyperbolic equations with delayed argument

Assanova, A. T.; Iskakova, N.B.; Orumbayeva, N.T.

doi:10.31489/2018m1/8-14

Cited by 7 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that the results and methods obtained in this paper can be extended to nonlinear nonlocal boundary value problems for the hyperbolic equation with finite time delay [20, 21], as well as on the optimal control problems of time‐delay systems [22–25].…”

Section: Discussionmentioning

confidence: 99%

On a problem for a delay differential equation

Iskakova

Temesheva

Uteshova

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

On a problem for a delay differential equation

Iskakova

Temesheva

Uteshova

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…A fitted spline method is implemented for the solution of these problems. In [22], it is established that the family of periodic boundary value issues for the system of ordinary differential equations with delayed argument and the periodic boundary value problem for the system of hyperbolic equations with delayed argument are related. The construction and convergence of algorithms for solving the comparable problem are demonstrated.…”

Section: Introductionmentioning

confidence: 99%

A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay

Srinivas,

Phaneendra

2024

View full text Add to dashboard Cite

A trigonometric spline based computational technique is suggested for the numerical solution of layer behavior differential-difference equations with a fixed large delay. The continuity of the first order derivative of the trigonometric spline at the interior mesh point is used to develop the system of difference equations. With the help of singular perturbation theory, a fitting parameter is inserted into the difference scheme to minimize the error in the solution. The method is examined for convergence. We have also discussed the impact of shift or delay on the boundary layer. The maximum absolute errors in comparison to other approaches in the literature are tallied, and layer behavior is displayed in graphs, to demonstrate the feasibility of the suggested numerical method.

show abstract

“…where a(x, t) = 1 2 ∂ ∂t ln f (x, t). Such problems these were investigated in the works [3][4][5][6]. We introduce a new unknown function w(x, t) = ∂u(x,t) ∂x , and the problem ( 5)-( 8) can be written in the form…”

Section: Introductionmentioning

confidence: 99%

On the solvability of a semi-periodic boundary value problem for the nonlinear Goursat equation

Orumbayeva¹,

Tokmagambetova²,

Nurgalieva³

2021

Bul. Kar. Univ. - Math.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Well-posedness of a periodic boundary value problem for the system of hyperbolic equations with delayed argument

Cited by 7 publications

References 0 publications

On a problem for a delay differential equation

On a problem for a delay differential equation

A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay

On the solvability of a semi-periodic boundary value problem for the nonlinear Goursat equation

Contact Info

Product

Resources

About