The Jacobi and Gauss-Seidel iterative methods are among iterative methods for solving linear system of equations. In this paper, a new iterative method is introduced, it is based on the linear combination of old and most recent calculated solutions. The new method can be considered as a general method, where the Jacobi and Gauss-Seidel methods as two special cases of it. Some convergence proper...

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

A family of simple derivative-free multipoint iterative methods, based on the interpolating polynomials, for solving nonlinear equations is presented. It is shown that the presented n-point iterative method has the convergence order 2n−1 with n function evaluations per iteration. It is an optimal iterative method in the sense of the Kung-Traub’s conjecture. Numerical examples are included to su...

Let C be a nonempty closed convex subset of a real Banach space E. Let S : C → C be a quasi-nonexpansive mapping, let T : C → C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F := {x ∈ C : Sx = x and Tx = x} 6 = ∅. Let {xn}n≥0 be the sequence generated from an arbitrary x0 ∈ C by xn+1 = (1− cn)Sxn + cnT xn, n ≥ 0. We prove necessary and sufficient conditions fo...

The purpose of this paper is to introduce a modified Halpern-type iteration algorithm and prove strong convergence of the algorithm for quasi-φ-asymptotically non-expansive mappings. Our results improve and extend the corresponding results announced by many others.

This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform...

K e y w o r d s N o n l i n e a r equations, Iteration method, Root finding, Order of convergence. 1. I N T R O D U C T I O N The problem of finding a real root of the nonlinear equation,

In this paper, we study the convergence of time-dependent Euler–Poisson equations to incompressible type Euler equations via the quasi-neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and the symmetric hyperbolic property of the systems are used to justify the convergence of the limit.

In this paper, we introduce a class of totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping to modify the Halpern-Mann-type iteration algorithm for a totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping, which has the strong convergence under a limit condition only in the framework of Banach spaces. Our results are applied to study the approximation probl...

In the last decades, the study of convergence conditions for the iterative methods based on splittings to solve de linear system Ax = b, has arisen in the works of many authors. We can consider that there are two principal kind of matrices: the nonnegative matrices, studied by authors as Varga [7], Berman and Plemmons [1], Marek and Szyld [5] and more recently by Climent and Perea [3], and the ...