Strong stability-preserving three-derivative Runge–Kutta methods

Qin, Xueyu; Jiang, Zhenhua; Yu, Jian; Huang, Lintao; Yan, Chao

doi:10.1007/s40314-023-02285-y

Cited by 6 publications

(4 citation statements)

References 36 publications

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“…This indicates that the ThDTSRK methods are computationally efficient for solving ordinary differential equations. In further studies, our proposed ThDTSRK schemes can be applied to partial differential equations which are reduced to ordinary differential equation system using various spatial discretization schemes [5,22]. The TDMSRK methods can demonstrate high computational efficiency, especially when employing high-order spatial discretization schemes.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, further information can be obtained from our source code [19]. 6 + 6 ŵT (c − e) 5 + 30 wT (c − e) 4 = 1+θ 7 ,…”

Section: Order Conditions Of Thdtsrk Methodsmentioning

confidence: 99%

“…In recent decades, there has been a concentrated effort to develop explicit stabilitypreserving discretization methods, while also achieving high-order convergence and superior computational efficiency. The discretization methods [5][6][7] that incorporate a combination of multistage, multistep, and multiderivative schemes offer an efficient pathway toward reaching these objectives. The main focus lies in establishing order conditions and ensuring numerical stability.…”

Section: Introductionmentioning

confidence: 99%

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Derivation of Three-Derivative Two-Step Runge–Kutta Methods

Qin,

Yu,

Yan

2024

Mathematics

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In this paper, we develop explicit three-derivative two-step Runge–Kutta (ThDTSRK) schemes, and propose a simpler general form of the order accuracy conditions (p≤7) by Albrecht’s approach, compared to the order conditions in terms of rooted trees. The parameters of the general high-order ThDTSRK methods are determined by utilizing the order conditions. We establish a theory for the A-stability property of ThDTSRK methods and identify optimal stability coefficients. Moreover, ThDTSRK methods can achieve the intended order of convergence using fewer stages than other schemes, making them cost-effective for solving the ordinary differential equations.

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Section: Discussionmentioning

confidence: 99%

“…Moreover, further information can be obtained from our source code [19]. 6 + 6 ŵT (c − e) 5 + 30 wT (c − e) 4 = 1+θ 7 ,…”

Section: Order Conditions Of Thdtsrk Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Derivation of Three-Derivative Two-Step Runge–Kutta Methods

Qin,

Yu,

Yan

2024

Mathematics

Self Cite

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“…Specifically, 'odesolve' is a component of our LE computation based on the Jacobian method. In contrast, ODE45 is a built-in official Matlab function based on the Runge-Kutta method [37], computing the system's trajectory under a given time range containing multi-steps. This specific parameter setting derives from a parallel random searching algorithm for parameter identification, which is based on the LE computation and the basic parameters of the Qi system.…”

Section: Basic Dynamic Behaviorsmentioning

confidence: 99%

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

Chen,

Yu,

Luo

et al. 2024

Mathematics

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Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications.

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A novel Lax–Wendroff type procedure of two-derivative time-stepping schemes for Euler and Navier–Stokes equations

Qin,

Zhang,

et al. 2025

Communications in Nonlinear Science and Numerical Simulation

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Strong stability-preserving three-derivative Runge–Kutta methods

Cited by 6 publications

References 36 publications

Derivation of Three-Derivative Two-Step Runge–Kutta Methods

Derivation of Three-Derivative Two-Step Runge–Kutta Methods

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

A novel Lax–Wendroff type procedure of two-derivative time-stepping schemes for Euler and Navier–Stokes equations

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