Product Description: The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e...read more

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Product Description: Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed...read more (view table of contents, read Amazon.com's description)

Product Description: The subject of this book is the solution of stiff differential equations and of differential-algebraic systems. This second edition contains new material including new numerical tests, recent progress in numerical differential-algebraic equations, and improved FORTRAN codes...read more

Product Description: This volume addresses some of the research areas in the general field of stability studies for differential equations, with emphasis on issues of concern for numerical studies. Topics considered include: (i) the long time integration of Hamiltonian Ordinary DEs and highly oscillatory systems, (ii) connection between stochastic DEs and geometric integration using the Markov chain Monte Carlo method, (iii) computation of dynamic patterns in evolutionary partial DEs, (iv) decomposition of matrices depending on parameters and localization of singularities, and (v) uniform stability analysis for time dependent linear initial value problems of ODEs...read more