## Numerical Methods for Ordinary Differential EquationsThis new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations. "This book is...an indispensible reference for any researcher."-American Mathematical Society on the First Edition. Features: * New exercises included in each chapter. * Author is widely regarded as the world expert on Runge-Kutta methods * Didactic aspects of the book have been enhanced by interspersing the text with exercises. * Updated Bibliography. |

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A-stable Adams—Bashforth algebraic Algorithm arrows assume behaviour bounded Butcher calculation coefficient coefﬁcients coeﬂicients components computed solution consider convergence corresponding deﬁned Deﬁnition denote difference equation eigenvalues elementary weight equal equivalent error constant error estimate Euler method evaluated exact solution example exists exp(z explicit factor Figure ﬁnal ﬁnd ﬁrst follows fourth order Hence implicit methods implicit Runge—Kutta methods initial value problem input integration iteration Lemma linear method linear multistep method Lipschitz condition Lobatto matrix method given method of order modiﬁed order conditions order method order star output Padé approximation Padé table possible preconsistency Proof quadrature formula quantities Radau result computed rooted trees Runge—Kutta method satisﬁes sequence signiﬁcant simpliﬁes solve speciﬁc stability function stability matrix stability region stage derivatives stage order stage values starting method step number stepsize h stiff problems Table tableau Taylor expansion Taylor series Theorem transformation truncation error vector write zero