Author(s)

Vembu Ananthaswamy, Lakshmanan Rajendran

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

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.

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

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.