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An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry

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  • A. H. Bhrawy
  • A. S. Alofi
  • R. A. Van Gorder

Abstract

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of power-law nonlinearity. In order to numerically solve this type of nonlinear boundary value problems, we construct a kind of spectral collocation method. The spatial approximation is based on shifted Jacobi polynomials with , and the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes for the spectral method. After deriving the method for a rather general class of equations, we apply it to several specific examples. One natural example is a nonlinear boundary value problem related to the Yamabe problem which arises in mathematical physics and geometry. A number of specific numerical experiments demonstrate the accuracy and the efficiency of the spectral method. We discuss the extension of the method to account for more complicated forms of nonlinearity.

Suggested Citation

  • A. H. Bhrawy & A. S. Alofi & R. A. Van Gorder, 2014. "An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, May.
    • Handle: RePEc:hin:jnlaaa:425648
    DOI: 10.1155/2014/425648
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    Cited by:

    1. Sabir, Zulqurnain & Saoud, Sahar & Raja, Muhammad Asif Zahoor & Wahab, Hafiz Abdul & Arbi, Adnène, 2020. "Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 534-548.

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