Numerical Initial Value Problems in Ordinary Differential Equations

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerical Integration of Initial Value Problems in Ordinary Differential Equations

The approach described in the first part of this paper is extended to include diagonally implicit Runge-Kutta (DIRK) formulae. The algorithms developed are suitable for the numerical integration of stiff differential systems, and their efficiency is illustrated by means of some numerical examples.

متن کامل

Numerical Ordinary Differential Equations - Boundary Value Problems

Consider a second-order linear 2-point boundary value problem (BVP) −z + p(x)z + q(x)z = r(x) (10.1) z(a) = α (10.2) z(b) = β (10.3) where p(x), q(x) and r(x) are given. By defining y(x) := [z(x), z (x)] T , the problem can be changed into a first-order differential system y = 0 1 q(x) p(x) y + 0 −r(x) (10.4) y 1 (a) − α = 0 (10.5) y 2 (b) − β = 0. (10.6) Remark. In general, a linear 2-point BV...

متن کامل

Validated solutions of initial value problems for ordinary differential equations

Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors survey Taylor series methods for validated so...

متن کامل

22 Initial Value Problems for Ordinary Differential Equations

We may be interested in the solution u(t) in a finite interval [t0, T ] or in the semi-infinite interval t ≥ t0. In most of this lecture f and u are real-valued functions. A generalization to vector-valued functions is important in applications and will be discussed at the end of the lecture. Numerical methods for the solution of the initial value problem (1)-(2) generate a sequence of values o...

متن کامل

Block Runge-Kutta Methods for the Numerical Integration of Initial Value Problems in Ordinary Differential Equations

Block Runge-Kutta formulae suitable for the approximate numerical integration of initial value problems for first order systems of ordinary differential equations are derived. Considered in detail are the problems of varying both order and stepsize automatically. This leads to a class of variable order block explicit Runge-Kutta formulae for the integration of nonstiff problems and a class of v...

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

ژورنال

عنوان ژورنال: The Computer Journal

سال: 1972

ISSN: 0010-4620,1460-2067

DOI: 10.1093/comjnl/15.2.155