ISSN:
1572-9125
Keywords:
Differential equations
;
Quadrature method
;
A-stability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A class of methods for the numerical solution of systems of ordinary differential equations is given which—for linear systems—gives solutions which conserve the stability property of the differential equation. The methods are of a quadrature type $$y_{i,r} = y_{n,r - 1} + h\sum\limits_{k = 1}^n {a_{ik} f(y_{k,r} ), n = 1,2, \ldots ,n, r = 1,2, \ldots ,} y_{n,0} given$$ wherea ik are quadrature coefficients over the zeros ofP n −P n−1 (v=1) orP n −P n−2 (v=2), whereP n is the Legendre polynomial orthogonal on [0,1] and normalized such thatP m (1)=1. It is shown that $$\left| {y_{n,r} - y(rh) = 0(h^{2n - _v } )} \right|$$ wherey is the solution of $$\frac{{dy}}{{dt}} = f(y), t \mathbin{\lower.3ex\hbox{$\buildrel〉\over{\smash{\scriptstyle=}\vphantom{_x}}$}} 0, y(0) given.$$
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01946812
Permalink
