Solutions of 2-D Bratu Equations Using Lie Group Method

Abstract

In this study, the nonlinear term in the two-dimensional Bratu equation has been replaced by its Taylor’s expansion. Hence, the resulting nonlinear partial differential equation has been studied using the Lie group method. The symmetry reductions that reduce nonlinear partial differential equations to ordinary differential equations are determined using the Lie group theory. The resultant ordinary differential equations were analytically solved, and the solutions were obtained in closed form for some specified parameter values, while others were solved numerically. We investigated the effect of increasing the value of the coefficient of the nonlinear term on the behavior of the solution in the obtained results, and the solutions were graphically presented.

Keywords

• two-dimensional Bratu equation
• Lie group
• similarity solutions
• differential transformation method