Applying differential transformation method to the one-dimensional planar Bratu problem

This paper is application of differential transformation method (DTM) to solve Bratu 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 unit square with u = 0 on 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 fixed point of hyperbolic cotangent function. Two special cases of problem are illustrated by using technique and numerical results and conclusions will be presented. Mathematics Subject Classification: 74S30, 34B15