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# Newton methods

## ABAQUS - Does Newton's method affect the convergence rate of higher order incremental scheme such as RK4 implemented via UMAT?

Wed, 2012-08-01 01:02 - jack_lukHello everyone,

I'm currently doing an analysis on the convergence rate of an incremental model that I have implemented in ABAQUS using a UMAT. Here's the BIG lines of the problem:

**1)** In UMAT : Solution of a differential equation using explicit Runge-Kutta 4 (RK4), which has a 4th order convergence rate, yields the stress state "S". (In my problem, stresses are applied)

## Solving nonlinear equilibrium problem

Mon, 2010-06-21 05:30 - Bashir VenkattaHi!

I am trying to solve (for equilibrium points) a geometrically nonlinear problem of the form

f(u) = F

where u is the displacement and F is the load. At first I tried the plain

Newton method, with, perhaps obviously, limited success. I then tried to use

linesearch and trustregion strategies to improve the situation. Eventually, however,

I realized that I needed to use some form of continuation method. Though the most

commonly used methods in mechanics seems to be based on gradually increasing the

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