In this paper, we study the boundary value problem on unit circle for Bratu’s equation depending real parameter μ. From estimate, existence of non-negative solution is set. A numerical method suggested to justify theoretical result. It a combination adaptation finite difference and Gauss-Seidel allowing us obtain good approximation μc, with respect exact μc = λ 5.7831859629467.

Perturbation–iteration theory is systematically generated for both linear and nonlinear second-order differential equations and applied to Bratu-type equations. Different perturbation–iteration algorithms depending upon the number of Taylor expansion terms are proposed. Using the iteration formulas derived using different perturbation–iteration algorithms, new solutions of Bratu-type equations ...

In this study, the nonlinear term in two-dimensional Bratu equation has been replaced by its Taylor’s expansion. Hence, resulting partial differential studied using Lie group method. The symmetry reductions that reduce equations to ordinary are determined theory. resultant were analytically solved, and solutions obtained closed form for some specified parameter values, while others solved numer...