In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a ‘preconditioner’ we use nonlinear multigrid schemes such as the Full Approximation Scheme (FAS) [1]. The benefits of nonlinear multigrid used in combination with the new accelerator are illustrated by difficult nonlinear elliptic scalar problems, such as the Bratu problem, and for systems of nonlinear equations, s...

This paper deals with the boundary and initial value problems for the Bratu-type model by using the modified variational iteration method. The efficiency of this modified method is to provide the analytical or approximate solutions to linear and nonlinear equations without the integral related with nonlinear term, linearization or discretization, which makes it reliable for solving the nonlinea...

In this article, we discuss the numerical solution of Bingham-Bratu-Gelfand (BBG) problem, a non-smooth nonlinear eigenvalue problem associated with total variation integral and an exponential nonlinearity. Using fact that one can view as possible Lagrange multiplier constrained minimization from Calculus Variations, associate BBG initial value (dynamical flow), well suited to time-discretizati...

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 paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that...