Solving nonlinear equations is a problem that needs to be dealt with in the practical engineering application. This paper uses Block–Broyden method for solving large-scale nonlinear systems, and two preconditioners are applied for solving the underlying linear systems, including SSOR preconditioner as well as ASSOR method, which is based on SSOR. It discusses their implementation processes and ...

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...

In this work, we have developed a fourth order Newton-like method based on harmonic mean and its multi-step version for solving system of nonlinear equations. The new fourth order method requires evaluation of one function and two first order Fréchet derivatives for each iteration. The multi-step version requires one more function evaluation for each iteration. The proposed new scheme does not ...

In this paper, we study the boundary value problem on unit circle for Bratu’s equation depending real parameter μ. From estimate, existence of non-negative solution is set. A numerical method suggested to justify theoretical result. It a combination adaptation finite difference and Gauss-Seidel allowing us obtain good approximation μc, with respect exact μc = λ 5.7831859629467.