Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniform partitions, and an optimal collocation method are derived for solving Bratu-type equations. Numerical examples are presented to verify the efficiency and accuracy of these methods when compared to other nume...

Perturbation–iteration theory is systematically generated for both linear and nonlinear second-order differential equations and applied to Bratu-type equations. Different perturbation–iteration algorithms depending upon the number of Taylor expansion terms are proposed. Using the iteration formulas derived using different perturbation–iteration algorithms, new solutions of Bratu-type equations ...

Bratu‐type equation has wide applications in physics, finance, and other fields. Also, fractional analysis been a popular topic recently. It is difficult to find the analytical solution once we add operator on left side of equation. In this work, apply explicit implicit finite difference methods solve Bratu From numerical examples, will see that not accurate, based Newton's method efficient som...

In this paper, we applied Exp-function method to some nonlinear evolution equations. The solution procedure of this method, by the help of symbolic computation of Matlab, Mathematica or so on, is of utter simplicity. The obtained results show that Exp-function method is very powerful and convenient mathematical tool for nonlinear evolution equations in science and engineering. Key WordsExp-func...

The aim of this study is applying the Multistage Adomian Decomposition Method (MADM), based on the Adomian Decomposition Method (ADM) to solve an initial value problem of Bratu-type. The approximat-ed solutions are computed and then the numerical results compared those of ADM, Finally comparisons of the results show that the pro-posed method is very effective and accurate.

In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a `precon-ditioner' we use nonlinear multigrid schemes, like FAS 1]. The beneets of the combination of nonlinear multigrid and the new proposed accelerator is shown for diicult nonlinear ellip-tic scalar problems, like the Bratu problem and for systems of nonlinear equations, like the Navier-Stokes equations.

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.

By using the integral operational matrix and the product operation matrix of the Chebyshev wavelet, a class of nonlinear fractional integral-differential equations of Bratu-type is transformed into nonlinear algebraic equations, which makes the solution process and calculation more simple. At the same time, reliable approaches for uniqueness and convergence of the Chebyshev wavelet method are d...