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The Construction of Finite Difference Approximations to Ordinary Differential Equations

Eusebius J. Doedel
SIAM Journal on Numerical Analysis
Vol. 15, No. 3 (Jun., 1978), pp. 450-465
Stable URL: http://www.jstor.org/stable/2156577
Page Count: 16
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The Construction of Finite Difference Approximations to Ordinary Differential Equations
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Abstract

Finite difference approximations of the form ∑sji = -rj dj,iuj + i = ∑mji = 1 ej,if(zj,i) for the numerical solution of linear nth order ordinary differential equations are analyzed. The order of these approximations is shown to be at least rj + sj + mj - n, and higher for certain special choices of the points zj,i. Similar approximations to initial or boundary conditions are also considered and the stability of the resulting schemes is investigated.

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