IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n715756.html

New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second‐Order Differential Equations Involving Singular and Bratu Type Equations

Author

Listed:
  • W. M. Abd-Elhameed
  • E. H. Doha
  • Y. H. Youssri

Abstract

A new spectral algorithm based on shifted second kind Chebyshev wavelets operational matrices of derivatives is introduced and used for solving linear and nonlinear second‐order two‐point boundary value problems. The main idea for obtaining spectral numerical solutions for these equations is essentially developed by reducing the linear or nonlinear equations with their initial and/or boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. Convergence analysis and some efficient specific illustrative examples including singular and Bratu type equations are considered to demonstrate the validity and the applicability of the method. Numerical results obtained are compared favorably with the analytical known solutions.

Suggested Citation

  • W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second‐Order Differential Equations Involving Singular and Bratu Type Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:715756
    DOI: 10.1155/2013/715756
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/715756
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/715756?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
    ---><---

    References listed on IDEAS

    as
    1. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, October.
    2. N. Daoudi-Merzagui & F. Derrab & A. Boucherif, 2012. "Subharmonic Solutions of Nonautonomous Second Order Differential Equations with Singular Nonlinearities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second‐Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. N. Daoudi-Merzagui & F. Derrab & A. Boucherif, 2012. "Subharmonic Solutions of Nonautonomous Second Order Differential Equations with Singular Nonlinearities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, March.
    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. W. M. Abd-Elhameed & Y. H. Youssri, 2014. "New Ultraspherical Wavelets Spectral Solutions for Fractional Riccati Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    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. A. H. Bhrawy, 2014. "A New Legendre Collocation Method for Solving a Two‐Dimensional Fractional Diffusion Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Fengying Zhou & Xiaoyong Xu, 2017. "Numerical Solution of Time‐Fractional Diffusion‐Wave Equations via Chebyshev Wavelets Collocation Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    3. Xiuling Yin & Yanqin Liu, 2014. "Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. A. H. Bhrawy & M. A. Alghamdi & Eman S. Alaidarous, 2014. "An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. W. M. Abd-Elhameed & Y. H. Youssri, 2014. "New Ultraspherical Wavelets Spectral Solutions for Fractional Riccati Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. W. M. Abd-Elhameed, 2015. "Some Algorithms for Solving Third‐Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2013:y:2013:i:1:n:715756. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.