A Computational Method for Solving the Boundary Value Problem for Impulsive Systems of Essentially Loaded Differential Equations

Kadirbayeva, Zh. M.; Kabdrakhova, S. S.; Mynbayeva, S. T.

doi:10.1134/s1995080222030131

Cited by 8 publications

(2 citation statements)

References 19 publications

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“…Loaded differential equations (LDE) were investigated in [9], [10] and the references therewith. Numerous problems for LDE and methods for solving problems for LDE are considered in [11]- [16].…”

Section: Introductionmentioning

confidence: 99%

Modification of the Parametrization Method for Solving a Boundary Value Problem for Loaded Differential Epcag

Бакирова

Kadirbayeva²,

Nessipbayeva³

2022

JMMCS

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The functional differential equation plays important role in mathematical modeling of biological problems. In the present research work, we investigate a boundary value problem (BVP) for a functional differential equation. This equation includes loaded terms and a term with generalized piecewise constant argument. We apply a modified version of the Dzhumabaev parameterization method. The method's goal is to lead the original problem into an equivalent multi-point BVP for ordinary differential equations with parameters, which is composed of a problem with initial and additional conditions. The multi-point BVP is leaded to a system of linear algebraic equations in parameters, which are introduced as the values of the desired solution at the dividing points. The found parameters are plugged into auxiliary Cauchy problems on the partition subintervals, whose solutions are the restrictions of the solution to the original problem. The obtained results are verified by a numerical example. Numerical analysis showed high efficiency of the constructed modified version of the Dzhumabaev parameterization method.

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Section: Introductionmentioning

confidence: 99%

Modification of the Parametrization Method for Solving a Boundary Value Problem for Loaded Differential Epcag

Бакирова

Kadirbayeva²,

Nessipbayeva³

2022

JMMCS

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“…The study of loaded differential equations is of interest both from the practical and theoretical points of view, in mathematical modeling and in general mathematics itself. In [1][2][3][4][5][6][7][8][9], various boundary-value problems for loaded differential equations are studied and solved by different methods.…”

Section: Introductionmentioning

confidence: 99%

A novel numerical implementation for solving problem for loaded DEPCAG

Kadirbayeva

Uteshova

Marat

et al. 2022

ijmph

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In this work, we propose a new computational approach is implemented to solve a two-point BVP for a loaded differential equation with piecewise constant argument of generalized type (DEPCAG) based on the Dzhumabaev parameterization method. In this method, as parameters, we take the values of the desired solution at the partition points which are chosen taking into account the specifics o f the equation. The problem under consideration reduces to an equivalent parametric problem for ordinary differential equations. A solution to this problem, which in turn are found from a system of linear algebraic equations. The found values of the parameters are used to determine the values of the unknown function at the remaining points of the interval by solving auxiliary initial-value problems. We develop a novel numerical implementation for solving the considered a two-point BVP for loaded DEPCAG and provide two examples illustrating its application, where Mathcad software will be used for the calculation.

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A Computational Method for Solving a Boundary-Value Problem for Differential Equations with Piecewise Constant Argument of Generalized Type

Бакирова

Kadirbayeva

Salgarayeva

2022

Lobachevskii J Math

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A Computational Method for Solving the Boundary Value Problem for Impulsive Systems of Essentially Loaded Differential Equations

Cited by 8 publications

References 19 publications

Modification of the Parametrization Method for Solving a Boundary Value Problem for Loaded Differential Epcag

Modification of the Parametrization Method for Solving a Boundary Value Problem for Loaded Differential Epcag

A novel numerical implementation for solving problem for loaded DEPCAG

A Computational Method for Solving a Boundary-Value Problem for Differential Equations with Piecewise Constant Argument of Generalized Type

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