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

AM > Vol.3 No.9, September 2012

Applied Mathematics

Volume 3, Issue 9 (September 2012)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

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

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Download as PDF (Size: 3086KB) PP. 1044-1058

DOI: 10.4236/am.2012.39154 5,367 Downloads 9,621 Views Citations

Author(s)

Vembu Ananthaswamy, Lakshmanan Rajendran

Affiliation(s)

Department of Mathematics, The Madura College, Madurai, India.

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.

KEYWORDS

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

Share and Cite:

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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