APPLYING DIFFERENTIAL TRANSFORMATION METHOD TO THE ONE-DIMENSIONAL PLANAR BRATU PROBLEM

This paper is the application of differential transformation method (DTM) to solve the Bratu problem. A considerable research works have been conducted recently in applying DTM to different types of partial differential equation of Abdel-Halim Hassan (Chaos, Solitons & Fractals [6]) and fractional differential equations of Arikoglu and Ozkol (Chaos, Solitons & Fractals [1]). The nonlinear eigenvalue problem 0 = + Δ u e u λ in the unit square with u = 0 on the boundary 1494 I. H. Abdel-Halim Hassan and Vedat Suat Erturk is often referred to as "the Bratu problem". The Bratu problem in one-dimensional planar coordinates 0 = + ′ ′ u e u λ with u(0) = u(1) = 0 has two known, bifurcated solutions for values of c λ λ and a unique solution when c λ λ = . The value of c λ is related to the fixed point of hyperbolic cotangent function. Two special cases of the problem are illustrated by using the technique and numerical results and conclusions will be presented. Mathematics Subject Classification: 74S30, 34B15