Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation

Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation

We give an analysis of a continuation algorithm for the numerical solution of the forcebased quasicontinuum equations. The approximate solution of the force-based quasicontinuum equations is computed by an iterative method using an energy-based quasicontinuum approximation as the preconditioner. The analysis presented in this paper is used to determine an efficient strategy for the parameter st...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

On the Iterative Solution of Adjoint Equations

High order quadrature based iterative method for approximating the solution of nonlinear equations

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI =...

Iterative solution of two matrix equations

We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations X + A∗X−1A = Q and X − A∗X−1A = Q, where Q is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton’s method and inversion free variants of the basic fixed point iteration are discussed in some detail for the...