The Adomian Decomposition Method (ADM) has been applied to a wide class of problems in physics, biology and chemical reactions. The method provides the solution in a rapid convergent series with computable terms. This method was successfully applied to nonlinear differential delay equations [1], a nonlinear dynamic systems [2], the heat equation [3,4], the wave equation [5], coupled nonlinear p...

We describe a parallel algorithm for the numerical computation of guaranteed bounds for solutions of elliptic boundary value equations of second order. We use C 2-Hermite-elements and a parallel Newton multigrid method to produce approximations of high accuracy. Then, we compute upper bounds for the defect and enclosures for the eigenvalues of the linearization. In order to obtain veriied bound...

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of...

In this study, the nonlinear term in two-dimensional Bratu equation has been replaced by its Taylor’s expansion.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...

In this paper, we present a reliable framework to solve the initial and boundary value problems of Bratu-type which are widely applicable in fuel ignition of the combustion theory and heat transfer. The algorithm rests mainly on a relatively new technique, the variational iteration method. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm.

We describe a parallel algorithm for the numerical computation of guaranteed bounds for solutions of elliptic boundary value equations of second order. We use C 2-Hermite elements and a parallel Newton multigrid method to produce approximations of high accuracy. Then, we compute upper bounds for the defect and enclosures for the eigenvalues of the linearization. In order to obtain veriied bound...