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

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DOI: 10.4236/am.2012.39154    4,051 Downloads   7,156 Views   Citations

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.

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The authors declare no conflicts of interest.

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V. Ananthaswamy and L. Rajendran, "Analytical Solutions of Some Two-Point Non-Linear Elliptic Boundary Value Problems," Applied Mathematics, Vol. 3 No. 9, 2012, pp. 1044-1058. doi: 10.4236/am.2012.39154.

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