Numerical Solution to a Control Problem for Integro-Differential Equations

Assanova, A. T.; Бакирова, Е. А.; Kadirbayeva, Zh. M.

doi:10.1134/s0965542520020049

Cited by 33 publications

(15 citation statements)

References 14 publications

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“…We use the approach offered in [16][17][18][19][20][21] to solve the boundary value problem ( 5), ( 6). This approach based on the algorithms of the parameterization method and numerical methods for solving Cauchy problems.…”

Section: Scheme Of Parametrization Methodmentioning

confidence: 99%

“…It is not difficult to establish that the solvability of the boundary value problem ( 5), ( 6) is equivalent to the solvability of the system (20). The solution of the system (20) is a vector * * , * , … , * ∈ consists of the values of the solutions of the original problem (5), (6) We use the numerical implementation of algorithm.…”

Section: Scheme Of Parametrization Methodmentioning

confidence: 99%

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An Algorithm for Solving a Boundary Value Problem for Essentially Loaded Differential Equations

Kadirbayeva

Бакирова

Dauletbayeva

et al. 2021

News of NAN RK. SGTS

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A linear boundary value problem for essentially loaded differential equations is considered. Using the properties of essentially loaded differential we reduce the considering problem to a two-point boundary value problem for loaded differential equations. This problem is investigated by parameterization method. We offer algorithm for solving to boundary value problem for the system of loaded differential equations. This algorithm includes of the numerical solving of the Cauchy problems for system of the ordinary differential equations and solving of the linear system of algebraic equations. For numerical solving of the Cauchy problem we apply the Runge–Kutta method of 4th order. The proposed numerical implementation is illustrated by example.

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Section: Scheme Of Parametrization Methodmentioning

confidence: 99%

Section: Scheme Of Parametrization Methodmentioning

confidence: 99%

An Algorithm for Solving a Boundary Value Problem for Essentially Loaded Differential Equations

Kadirbayeva

Бакирова

Dauletbayeva

et al. 2021

News of NAN RK. SGTS

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“…In [4] we also propose a numerically approximate method for solving Cauchy problems for ordinary differential equations on subintervals, which is illustrated by numerical examples. The authors can present numerical results obtained using MathCad15.…”

Section: Algorithms For Solving a Problem With A Parameter For A Loadmentioning

confidence: 99%

“…Let the problem (5.1)-(5.2) be well-posed with the constant χ 0 . Then there exists a number h 1 > 0 such that for all h ∈ (0, h 1 ] : 2N h = T , the (n(2N + 1) + l) × (n(2N + 1) + l) matrix Q * (δ 2N (h)) is invertible, and the estimate[Q * (δ 2N (h))] −1 ≤ 2χ 0 /h (5.8)is true.The proofs of Theorems 11 and 12 with slight modifications are similar to the proofs of Theorems 4.1 and 4.2, respectively, in[4]. So, if problem (5.1)-(5.2) is well-posed with the constant χ 0 , then inequalities (5.7) and (5.8) yield the estimatecond ∞ Q * (δ 2N (h)) = Q * (δ 2N (h)) • [Q * (δ 2N (h))] −1 ≤2χ 0 h max h( B 0 + B + C ), 1 + (1 + βT h + α 0 h) exp(αh) (5.9)…”

mentioning

confidence: 93%

“…The theory of control problems for a system of ordinary differential equations and for a system of integro-differential equations in partial derivatives, with parameters, is rapidly developing and used in various fields of applied mathematics, biophysics, biomedicine, chemistry, etc. Control problems, also called as boundary value problems with parameters and parameter identification problems for systems of ordinary differential and integro-differential equations with parameters, are intensively studied by many authors [3,4,8,9,17,18,19,20,24,25]. To find solutions to these problems, methods of the qualitative theory of differential equations, variational calculus and optimization theory, the method of upper and lower solutions, etc.…”

Section: Introductionmentioning

confidence: 99%

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A Problem With Parameter for the Integro-Differential Equations

Бакирова

Assanova

Kadirbayeva

2021

Mathematical Modelling and Analysis

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The article proposes a numerically approximate method for solving a boundary value problem for an integro-differential equation with a parameter and considers its convergence, stability, and accuracy. The integro-differential equation with a parameter is approximated by a loaded differential equation with a parameter. A new general solution to the loaded differential equation with a parameter is introduced and its properties are described. The solvability of the boundary value problem for the loaded differential equation with a parameter is reduced to the solvability of a system of linear algebraic equations with respect to arbitrary vectors of the introduced general solution. The coefficients and the right-hand sides of the system are compiled through solutions of the Cauchy problems for ordinary differential equations. Algorithms are proposed for solving the boundary value problem for the loaded differential equation with a parameter. The relationship between the qualitative properties of the initial and approximate problems is established, and estimates of the differences between their solutions are given.

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Stochastic maximum principle for moving average control system

Li,

Han,

Gao

2023

Optim Control Appl Methods

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In this paper, we consider the stochastic optimal control problem for moving average control system. The corresponding moving average stochastic differential equation is a kind of integral differential equations. We prove the existence and uniqueness of the solution of the moving average stochastic differential equations. We obtain the stochastic maximum principle of the moving average optimal control system by introducing a kind of generalized anticipated backward stochastic differential equations. We prove the existence and uniqueness of the solution of this adjoint equation, which is singular at 0. As an application, the linear quadratic moving average control problem is investigated to illustrate the main results.

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Numerical Solution to a Control Problem for Integro-Differential Equations

Cited by 33 publications

References 14 publications

An Algorithm for Solving a Boundary Value Problem for Essentially Loaded Differential Equations

An Algorithm for Solving a Boundary Value Problem for Essentially Loaded Differential Equations

A Problem With Parameter for the Integro-Differential Equations

Stochastic maximum principle for moving average control system

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