Equilibrium States for Multistep Methods Department of Mathematics Equilibrium States for Multistep Methods

نویسندگان

  • G Hall
  • George Hall
چکیده

When the stepsize in non-stii ODE codes is restricted by stability, an uneven pattern of stepsizes with many step rejections is frequently observed. Results analysing this behaviour have been obtained for Runge-Kutta methods, leading to several papers attempting to improve stepsize control. It is shown here that a similar analysis can be carried out for mul-tistep methods. The explicit Adams 2-step method is used to illustrate the techniques required.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Free and constrained equilibrium states in a variational problem on a surface

We study the equilibrium states for an energy functional with a parametric force field on a region of a surface. Consideration of free equilibrium states is based on Lyusternik - Schnirelman's and Skrypnik's variational methods. Consideration of equilibrium states under a constraint of geometrical character is based on an analog of Skrypnik's method, described in [P. Vyridis, {it Bifurcation in...

متن کامل

Superconvergence analysis of multistep collocation method for delay functional integral equations

In this paper, we will present a review of the multistep collocation method for Delay Volterra Integral Equations (DVIEs) from [1] and then, we study the superconvergence analysis of the multistep collocation method for DVIEs. Some numerical examples are given to confirm our theoretical results.

متن کامل

‎Multistep collocation method for nonlinear delay integral equations

‎The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the...

متن کامل

Equilibrium attractive properties of a class of multistep Runge-Kutta methods

The main purpose of this paper is to discuss the equilibrium attractive properties of a class of multistep Runge–Kutta methods for initial value problems of ordinary differential equations. Some algebraic conditions insuring the equilibrium attractivity are given, and some methods satisfying these algebraic conditions are constructed. Some numerical examples confirm our results. 2005 Elsevier I...

متن کامل

A new two-step Obrechkoff method with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrodinger equation and related IVPs with oscillating solutions

A new two-step implicit linear Obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrodinger equation and related problems. This algorithm belongs in the category of the multist...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1995