Abstract
We continue to quote from this nice paper: “To integrate a system of n differential equations, an implicit method with a full s × s matrix requires the solution of ns simultaneous implicit (in general nonlinear) equations in each time step (...) One way to circumvent this difficulty is to use a lower triangular matrix (a ij )(i.e., a matrix with a ij = 0 for i < j); the equations may then be solved in s successive stages with only an n -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 diagonally implicit (DIRK).
... they called their methods “diagonally implicit”, a term which is reserved here for the special case where all diagonal entries are equal ...
(R. Alexander 1977)
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© 1996 Springer-Verlag Berlin Heidelberg
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Hairer, E., Wanner, G. (1996). Diagonally Implicit RK Methods. In: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05221-7_6
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DOI: https://doi.org/10.1007/978-3-642-05221-7_6
Publisher Name: Springer, Berlin, Heidelberg
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