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Titlebook: Solving Ordinary Differential Equations II; Stiff and Differenti Ernst Hairer,Gerhard Wanner Book 1996Latest edition Springer-Verlag Berlin

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Order Starsrder with real poles, comparison of stability domains (Jeltsch & Nevanlinna 1981, 1982), order bounds for hyperbolic or parabolic difference schemes (e.g., Iserles & Strang 1983, Iserles & Williamson 1983, Jeltsch 1988).
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Diagonally Implicit RK Methods triangular matrix (..)(i.e., a matrix with ..= 0 for . < .); the equations may then be solved in . successive stages with only an . -dimensional system to be solved at each stage”. In accordance with many authors, and in disaccordance with others (see above), we call such a method . (DIRK).
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Rosenbrock-Type Methodsmethods which try to avoid nonlinear systems and replace them by a sequence of linear systems. We therefore call these methods .. In the literature such methods are often called “semi-implicit” (or was it “semi-explicit”?), or “generalized” or “modified” or “adaptive” or “additive” Runge-Kutta methods.
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Diagonally Implicit RK Methodse solution of . simultaneous implicit (in general nonlinear) equations in each time step (...) One way to circumvent this difficulty is to use a lower triangular matrix (..)(i.e., a matrix with ..= 0 for . < .); the equations may then be solved in . successive stages with only an . -dimensional syst
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