𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The RKGL method for the numerical solution of initial-value problems

✍ Scribed by J.S.C. Prentice

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
188 KB
Volume
213
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

We introduce the RKGL method for the numerical solution of initial-value problems of the form y =f (x, y), y(a)= . The method is a straightforward modification of a classical explicit Runge-Kutta (RK) method, into which Gauss-Legendre (GL) quadrature has been incorporated. The idea is to enhance the efficiency of the method by reducing the number of times the derivative f (x, y) needs to be computed. The incorporation of GL quadrature serves to enhance the global order of the method by, relative to the underlying RK method. Indeed, the RKGL method has a global error of the form Ah r+1 + Bh 2m , where r is the order of the RK method and m is the number of nodes used in the GL component. In this paper we derive this error expression and show that RKGL is consistent, convergent and strongly stable.

πŸ“œ SIMILAR VOLUMES

An exponentially-fitted and trigonometri
An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems
✍ A. Konguetsof; T.E. Simos πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 367 KB

The new method is exponentially fitted and trigonometrically-fitted and is of algebraic order eight. The effectiveness of the exponential fitting is proved by the application of the new method and the classical one (with constant coefficients) to well-known periodic problems. (~) 2003 Elsevier Scien

Numerical solution of random differentia
Numerical solution of random differential initial value problems: Multistep methods
✍ J. C. CortΓ©s; L. JΓ³dar; L. Villafuerte πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 202 KB

This paper deals with the construction of numerical methods of random initial value problems. Random linear multistep methods are presented and sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations processes are computed in several

Continuous numerical solution of coupled
Continuous numerical solution of coupled parabolic initial value problems
✍ J.I. CastaΓ±o; L. JΓ³dar; E. Ponsoda; J.A.C. SΓ‘nchez πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 320 KB

This paper deals with the construction of continuous numerical solutions of coupled parabolic initial value problems using Fer's factorization and the Fourier transform approach.