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Fast Integration Of One-Dimensional Boundary Value Problems

Author

Listed:
  • RAFAEL G. CAMPOS

    (Facultad de Ciencias Físico-Matemáticas, Edificio Alfa, Universidad Michoacana, 58060, Morelia, Michoacán, México)

  • RAFAEL GARCÍA RUIZ

    (Facultad de Ciencias Físico-Matemáticas, Edificio Alfa, Universidad Michoacana, 58060, Morelia, Michoacán, México)

Abstract

Two-point nonlinear boundary value problems (BVPs) in both unbounded and bounded domains are solved in this paper using fast numerical antiderivatives and derivatives of functions ofL2(-∞, ∞). This differintegral scheme uses a new algorithm to compute the Fourier transform. As examples we solve a fourth-order two-point boundary value problem (BVP) and compute the shape of the soliton solutions of a one-dimensional generalized Korteweg–de Vries (KdV) equation.

Suggested Citation

  • Rafael G. Campos & Rafael García Ruiz, 2013. "Fast Integration Of One-Dimensional Boundary Value Problems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(11), pages 1-10.
    • Handle: RePEc:wsi:ijmpcx:v:24:y:2013:i:11:n:s0129183113500824
    DOI: 10.1142/S0129183113500824
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    Cited by:

    1. Campos, Rafael G. & Huet, Adolfo, 2018. "Numerical inversion of the Laplace transform and its application to fractional diffusion," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 70-78.
    2. Campos, Rafael G. & Marcellán, Francisco, 2017. "Quadratures and integral transforms arising from generating functions," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 8-18.

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