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

By I. H. Hassan, V. S. Erturk. 2007

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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

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/665d9067213ab32de3c3fd01b3c5c0ae057fa21b

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Citations in the corpus

A Reliable Analytical Method for Solving Higher-Order Initial Value Problems (2013, methodology): “The Bratu model appears in a number of applications such as the fuel ignition of the thermal combustion theory, the model of the thermal reaction process, the Chandrasekhar model of the expansion of the universe, questions in geometry and relativity concerning the Chandrasekhar model, chemical react”
A novel operational matrix method based on shifted Legendre polynomials for solving second-order boundary value problems involving singular, singularly perturbed and Bratu-type equations (2015, methodology): “In recent years, it has been a popular testbed for numerical and perturbation methods [21–27].”
The Lie-group shooting method for solving the Bratu equation (2011, methodology): “[13] have applied differential transformation method to the one-dimensional planar Bratu problem.”