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P example 336 according to table 332 the roots of p2 x

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Unformatted text preview: e collocation points ci, i = 1 2 : : : s, determined, the coe cients aij and bj , i j = 1 2 : : : s, may be determined from (3.3.15a,b). These maximal order collocation formulas are A-stable since they correspond to diagonal Pade approximations (Theorem 3.3.3). We may not want to impose the maximal order conditions to obtain, e.g., better stability and computational properties. With Radau quadrature, we x one of the coefcients at an endpoint thus, we set either c1 = 0 or cs = 1. The choice c1 = 0 leads to methods with bounded regions of absolute stability. Thus, the methods of choice have cs = 1. They correspond to the subdiagonal Pade approximations and are, hence, Aand L-stable (Theorem 3.3.3). They have orders of p = 2s ; 1 17], Section IV.5. Such excellent stability and accuracy properties makes these methods very popular for solving sti systems. The Radau polynomial of degree s on ;1 x 1 is Rs(x) = Ps(x) ; 2s s 1 Ps 1(x): ; The roots of Rs transformed to 0 1] (using = (1 + x)=2) are the ci, i + 1 2 : : :...
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