Titlebook: B-Series; Algebraic Analysis o John C. Butcher Book 2021 Springer Nature Switzerland AG 2021 Butcher series.Butcher group.numerical methods

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978-3-030-70958-7Springer Nature Switzerland AG 2021

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B-Series978-3-030-70956-3Series ISSN 0179-3632 Series E-ISSN 2198-3712

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https://doi.org/10.1007/978-1-4615-4639-9thods for their solution is essential. In this chapter a very basic survey of these important topics is presented. The fundamental theory of initial value problems is discussed, partly through a range of test problems. These problems arise from standard physical modelling, with the addition of a num

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https://doi.org/10.1007/978-1-4615-4639-9r free, trees. It is shown how to build up trees from the tree with a single vertex, using the beta-product and the B+ operation, together with a prefix (Polish) operator. Formal linear combinations of forests are introduced as the “forest space” and, as an application, the enumeration of trees is s

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Kornel Warwas,Krzysztof Augustynekings. One mapping would be the exact flow through a specified time step and the other would be a numerical scheme, such as a Runge–Kutta method. The B-series approach to questions like this is to write the Taylor expansions of the two mappings in a special way, in terms of “elementary differentials”

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Kornel Warwas,Krzysztof Augustynekting there is no interest in numerical methods which are applicable only to scalar problems and, above order 4, an analysis based on B-series is more appropriate. Even for order 5 there exist scalar methods with reduced order when applied to non-scalar problems. Explicit methods to order 5 are deriv

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