IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v354y2019icp353-364.html
   My bibliography  Save this article

Explicit Runge–Kutta methods for starting integration of Lane–Emden problem

Author

Listed:
  • Tsitouras, Ch.

Abstract

Traditionally, when constructing explicit Runge–Kutta methods we demand the satisfaction of the trivial simplifying assumption. Thus, f1=f(x0,y0) is always used as the first stage of these methods when applied to the Initial Value Problem (IVP): y′(x)=f(x,y),y(x0)=y0. Here we examine the case with f1=f(x0+c1h,y0),(h: the step) and c1 ≠ 0. We derive the order conditions for arbitrary order and construct a 5th order method at the standard cost of six stages per step. This method is found to outperform other classical Runge–Kutta pairs with orders 5(4) when applied to problems with singularity at the beginning (e.g. Lane–Emden problem).

Suggested Citation

  • Tsitouras, Ch., 2019. "Explicit Runge–Kutta methods for starting integration of Lane–Emden problem," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 353-364.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:353-364
    DOI: 10.1016/j.amc.2019.02.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319301511
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.02.047?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. D. F. Papadopoulos & T. E. Simos, 2013. "The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nyström Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, May.
    2. T. E. Simos, 2012. "Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-Lag," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, April.
    3. Junyan Ma & T. E. Simos, 2016. "Hybrid high algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(05), pages 1-20, May.
    4. T. E. Simos, 2012. "New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vladislav N. Kovalnogov & Ruslan V. Fedorov & Tamara V. Karpukhina & Theodore E. Simos & Charalampos Tsitouras, 2022. "Runge–Kutta Embedded Methods of Orders 8(7) for Use in Quadruple Precision Computations," Mathematics, MDPI, vol. 10(18), pages 1-12, September.

    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. Tsitouras, Ch. & Famelis, I.Th., 2018. "Bounds for variable degree rational L∞ approximations to the matrix exponential," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 376-386.
    2. Saleem Obaidat & Said Mesloub, 2019. "A New Explicit Four-Step Symmetric Method for Solving Schrödinger’s Equation," Mathematics, MDPI, vol. 7(11), pages 1-12, 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:eee:apmaco:v:354:y:2019:i:c:p:353-364. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.