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If the roots of the characteristic polynomial ρ all have modulus less than or equal to 1 and the roots of modulus 1 are of multiplicity 1, we say that the root condition is satisfied. A linear multistep method is zero-stable if and only if the root condition is satisfied ( Süli & Mayers 2003 , p. 335).
Lines perpendicular to line l are modeled by chords whose extension passes through the pole of l. Hence we draw the unique line between the poles of the two given lines, and intersect it with the boundary circle; the chord of intersection will be the desired common perpendicular of the ultraparallel lines.
Ernst Hairer and Gerhard Wanner, Solving ordinary differential equations II: Stiff and differential-algebraic problems, second edition, Springer Verlag, Berlin, 1996. ISBN 3-540-60452-9. (This two-volume monograph systematically covers all aspects of the field.) Hochbruck, Marlis; Ostermann, Alexander (May 2010). "Exponential integrators".
There are three main families of Lobatto methods, [6] called IIIA, IIIB and IIIC (in classical mathematical literature, the symbols I and II are reserved for two types of Radau methods). These are named after Rehuel Lobatto [ 6 ] as a reference to the Lobatto quadrature rule , but were introduced by Byron L. Ehle in his thesis. [ 7 ]
In numerical analysis, the Runge–Kutta methods (English: / ˈ r ʊ ŋ ə ˈ k ʊ t ɑː / ⓘ RUUNG-ə-KUUT-tah [1]) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. [2]
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6 1/2 -8/27 2 -3544/2565 1859/4104 ... "New high-order Runge-Kutta formulas with step size control for systems of first and second-order differential equations".
Kasparas Jakucionis made a tiebreaking layup with 32 seconds left, and No. 22 Illinois survived a furious comeback bid by Washington to squeak out an 81-77 victory Sunday. The Fighting Illini (11 ...
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