IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4291-d1260016.html
   My bibliography  Save this article

Explicit Symplectic Runge–Kutta–Nyström Methods Based on Roots of Shifted Legendre Polynomial

Author

Listed:
  • Jun Zhang

    (School of Science, East China Jiaotong University, Nanchang 330013, China)

  • Jingjing Zhang

    (School of Science, East China Jiaotong University, Nanchang 330013, China)

  • Shangyou Zhang

    (Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA)

Abstract

To date, all explicit symplectic Runge–Kutta–Nyström methods of order five or above are derived by numerical solutions of order condition equations and symplectic condition. In this paper, we derive 124 sets of seven-stage fifth-order explicit symplectic Runge–Kutta–Nyström methods with closed-form coefficients in the Butcher tableau using the roots of a degree-3 shifted Legendre polynomial. One method is analyzed and its P-stable interval is derived. Numerical tests on the two newly discovered methods are performed, showing their long-time stability and large step size stability over some existing methods.

Suggested Citation

  • Jun Zhang & Jingjing Zhang & Shangyou Zhang, 2023. "Explicit Symplectic Runge–Kutta–Nyström Methods Based on Roots of Shifted Legendre Polynomial," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4291-:d:1260016
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4291/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/20/4291/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tang, Wensheng & Zhang, Jingjing, 2018. "Symplecticity-preserving continuous-stage Runge–Kutta–Nyström methods," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 204-219.
    2. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Meng An & Haixiang Zhang, 2023. "High-Dimensional Mediation Analysis for Time-to-Event Outcomes with Additive Hazards Model," Mathematics, MDPI, vol. 11(24), pages 1-11, December.
    2. Abdumauvlen Berdyshev & Dossan Baigereyev & Kulzhamila Boranbek, 2023. "Numerical Method for Fractional-Order Generalization of the Stochastic Stokes–Darcy Model," Mathematics, MDPI, vol. 11(17), pages 1-27, September.
    3. Han-Sol Lee & Changgyun Jin & Chanwoo Shin & Seong-Eun Kim, 2023. "Sparse Diffusion Least Mean-Square Algorithm with Hard Thresholding over Networks," Mathematics, MDPI, vol. 11(22), pages 1-16, November.
    4. Elif Tan & Diana Savin & Semih Yılmaz, 2023. "A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields," Mathematics, MDPI, vol. 11(22), pages 1-14, November.
    5. Yongou Zhang & Zhongjian Ling & Hao Du & Qifan Zhang, 2023. "Finite-Difference Frequency-Domain Scheme for Sound Scattering by a Vortex with Perfectly Matched Layers," Mathematics, MDPI, vol. 11(18), pages 1-11, September.
    6. Ishtiaq Ali & Muhammad Yaseen & Muhammad Abdullah & Sana Khan & Fethi Bin Muhammad Belgacem, 2023. "An Innovative Numerical Method Utilizing Novel Cubic B-Spline Approximations to Solve Burgers’ Equation," Mathematics, MDPI, vol. 11(19), pages 1-19, September.
    7. Jiaqi Wang & Jianbing Su, 2023. "Boundedness and Compactness of Weighted Composition Operators from α -Bloch Spaces to Bers-Type Spaces on Generalized Hua Domains of the First Kind," Mathematics, MDPI, vol. 11(20), pages 1-27, October.
    8. Ismagil T. Habibullin & Aigul R. Khakimova & Alfya U. Sakieva, 2023. "Miura-Type Transformations for Integrable Lattices in 3D," Mathematics, MDPI, vol. 11(16), pages 1-15, August.
    9. Badriah Alamri, 2023. "Solving Integral Equation and Homotopy Result via Fixed Point Method," Mathematics, MDPI, vol. 11(21), pages 1-19, October.
    10. Salman Khalid & Jinwoo Song & Muhammad Muzammil Azad & Muhammad Umar Elahi & Jaehun Lee & Soo-Ho Jo & Heung Soo Kim, 2023. "A Comprehensive Review of Emerging Trends in Aircraft Structural Prognostics and Health Management," Mathematics, MDPI, vol. 11(18), pages 1-42, September.
    11. Jiří Holman, 2023. "Numerical Solution of Transition to Turbulence over Compressible Ramp at Hypersonic Velocity," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    12. Jianyu Wang & Chunhua Fang & Guifeng Zhang, 2023. "Multi-Effective Collocation Methods for Solving the Volterra Integral Equation with Highly Oscillatory Fourier Kernels," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    13. Qiu Lin & Ruisheng Qi, 2023. "Optimal Weak Order and Approximation of the Invariant Measure with a Fully-Discrete Euler Scheme for Semilinear Stochastic Parabolic Equations with Additive Noise," Mathematics, MDPI, vol. 12(1), pages 1-29, December.
    14. Jeffrey A. Hogan & Joseph D. Lakey, 2023. "Spatio–Spectral Limiting on Replacements of Tori by Cubes," Mathematics, MDPI, vol. 11(23), pages 1-14, November.
    15. Nazim & Nadeem Ur Rehman & Ahmad Alghamdi, 2023. "On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤ n," Mathematics, MDPI, vol. 11(20), pages 1-14, October.
    16. Li Cheng & Wen-Xiu Ma, 2023. "Similarity Transformations and Nonlocal Reduced Integrable Nonlinear Schrödinger Type Equations," Mathematics, MDPI, vol. 11(19), pages 1-8, September.
    17. Jagdish S. Thakur & Archana Thakur & Lawrence G. Lum, 2023. "Mathematical Model to Predict Polyclonal T-Cell-Dependent Antibody Synthesis Responses," Mathematics, MDPI, vol. 11(18), pages 1-19, September.
    18. Amira F. Daghistani & Ahmed M. T. Abd El-Bar & Ahmed M. Gemeay & Mahmoud A. E. Abdelrahman & Samia Z. Hassan, 2023. "A Hyperbolic Secant-Squared Distribution via the Nonlinear Evolution Equation and Its Application," Mathematics, MDPI, vol. 11(20), pages 1-17, October.
    19. Tang, Wensheng & Sun, Yajuan & Zhang, Jingjing, 2019. "High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 670-679.
    20. Sarfraz Nawaz Malik & Nazar Khan & Ferdous M. O. Tawfiq & Mohammad Faisal Khan & Qazi Zahoor Ahmad & Qin Xin, 2023. "Fuzzy Differential Subordination Associated with a General Linear Transformation," Mathematics, MDPI, vol. 11(22), pages 1-17, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4291-:d:1260016. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.