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J. P. Abbott, “An Efficient Algorithm for the Determination of Certain Bifurcation Point,” Journal of Computational and Applied Mathematics, Vol. 4, No. 1, 1978, pp. 19-27. doi:10.1016/0771-050X(78)90015-3

has been cited by the following article:

• TITLE: Analytical Solutions of Some Two-Point Non-Linear Elliptic Boundary Value Problems

  AUTHORS: Vembu Ananthaswamy, Lakshmanan Rajendran

  KEYWORDS: Two-Point Elliptic Boundary Value Problems; Bratu’s Equation; Troesch’s Problem; Non-Linear Equations; Homotopy Perturbation Method; Porous Catalyst; Numerical Simulation

  JOURNAL NAME: Applied Mathematics, Vol.3 No.9, September 27, 2012

  ABSTRACT: Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.