On the Non-Negative Radial Solutions of the Two Dimensional Bratu Equation

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

Matrix-valued Bratu equation and the exact solution of its initial value problem

A matrix-valued extension of the Bratu equation is defined. For its initial value problem, the exponential matrix solution and power series solution are provided.

Direct solution of uncertain bratu initial value problem

<span>In this paper, an approximate analytical solution for solving the fuzzy Bratu equation based on variation iteration method (VIM) is analyzed and modified without needed of any discretization by taking the benefits of fuzzy set theory. VIM is applied directly, without being reduced to a first order system, to obtain an approximate solution of the uncertain Bratu equation. An example in this regard have been solved to show the capacity and convenience of VIM.</span>