Runge–Kutta Methods for Systems of Differential Equation with Piecewise Continuous Arguments: Convergence and Stability

Wang, Qi; Wang, Xiaoming

doi:10.1080/01630563.2017.1421554

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…The application of the numerical integration method to solve ordinary differential equations was published by [8]. The numerical solution of SLDE was published by [9,11]. Matrix notation of the quaternion vector space was analysed by [1,7].…”

Section: Introductionmentioning

confidence: 99%

An algorithm for solving of Euler parameters differential equations system

Rédl¹

2021

MERAA

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The design an optimal numerical method for solving a system of ordinary differential equations simultaneously is described in this paper. System of differential equations was represented by a system of linear ordinary differential equations of Euler’s parameters called quaternions. The components of angular velocity were obtained by the experimental way. The angular velocity of the centre of gravity was determined from sensors of acceleration located in the plane of the centre of gravity of the machine. The used numerical method for solving was a fourth-order Runge-Kutta method. The stability of solving was based on the orthogonality of a direct cosine matrix. The numerical process was controlled on every step in numerical integration. The algorithm was designed in the C# programming language.

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Section: Introductionmentioning

confidence: 99%

An algorithm for solving of Euler parameters differential equations system

Rédl¹

2021

MERAA

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“…Although the numerical study of EPCA starts late, it has gradually become more and more popular since EPCA can hardly be solved by analytical methods or much complicated to deal with. Many numerical methods have been applied to EPCA, such as the θ-methods [26], the Runge-Kutta methods [24,35], the Euler-Maclaurin methods [18], spectral collocation methods [33] and the linear multistep methods [16] and so on.…”

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confidence: 99%

Convergence and Stability of Galerkin Finite Element Method for Hyperbolic Partial Differential Equation With Piecewise Continuous Arguments of Advanced Type

Chen,

Wang

2023

Mathematical Modelling and Analysis

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This paper deals with the convergence and stability of Galerkin finite element method for a hyperbolic partial differential equations with piecewise continuous arguments of advanced type. First of all, we obtain the expression of analytic solution by the method of separation variable, then the sufficient conditions for stability are obtained. Semidiscrete and fully discrete schemes are derived by Galerkin finite element method, and their convergence are both analyzed in L2-norm. Moreover, the stability of the two schemes are investigated. The semidiscrete scheme can achieve unconditionally stability. The sufficient conditions of stability for fully discrete scheme are derived under which the analytic solution is asymptotically stable. Finally, some numerical experiments are presented to illustrate the theoretical results.

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Numerical Bifurcation of a Delayed Diffusive Hematopoiesis Model with Dirichlet Boundary Conditions

Liu,

Wang

2024

Ukr Math J

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Runge–Kutta Methods for Systems of Differential Equation with Piecewise Continuous Arguments: Convergence and Stability

Cited by 5 publications

References 24 publications

An algorithm for solving of Euler parameters differential equations system

An algorithm for solving of Euler parameters differential equations system

Convergence and Stability of Galerkin Finite Element Method for Hyperbolic Partial Differential Equation With Piecewise Continuous Arguments of Advanced Type

Numerical Bifurcation of a Delayed Diffusive Hematopoiesis Model with Dirichlet Boundary Conditions

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