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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In numerical analysis, the Runge Kutta methods are an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations. These techniques were developed around 1900 by the German mathematicians C. Runge and M.W. Kutta. See the article on numerical ordinary differential equations for more background and other methods. See also List of Runge Kutta methods. One member of the family of Runge Kutta methods is so commonly used that it is often referred to as "RK4", "classical Runge-Kutta method" or simply as "the Runge Kutta method".

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Erscheinungsdatum: 21.01.2020, Medium: Buch, Einband: Gebunden, Titel: Graphical Methods, Autor: Runge, Carl, Verlag: Columbia University Press, Sprache: Englisch, Rubrik: Mathematik // Sonstiges, Seiten: 160, Informationen: HC runder Rücken kaschiert, Gewicht: 404 gr, Verkäufer: averdo

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This book deals with the derivation of diagonally implicit Runge-Kutta (DIRK) methods of order four and five which are specially designed for the integration of linear ordinary differential equations (LODEs). The restriction to LODEs with constant coefficients reduces the number of order equations which the coefficients of Runge-Kutta (RK) methods must satisfy. The coefficients of the RK methods are chosen such that the error norm is minimized, this resulted in methods which are almost one order higher than the actual order. The stability polynomials and stability regions of the methods are then obtained using MATHEMATICA package. Codes using C++ programming based on the methods are developed to test sets of problems on linear ordinary differential equations. Numerical results show that the new methods are more efficient than the existing methods.

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Erscheinungsdatum: 11/2011, Medium: Taschenbuch, Einband: Kartoniert / Broschiert, Titel: Diagonally Implicit Runge-Kutta Methods for Solving Linear ODEs, Titelzusatz: Numerical Methods for ODEs, Autor: Che Jawias, Nurizzati // Ismail, Fudziah, Verlag: LAP Lambert Acad. Publ., Sprache: Englisch, Rubrik: Mathematik // Sonstiges, Seiten: 140, Informationen: Paperback, Gewicht: 225 gr, Verkäufer: averdo

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Erscheinungsdatum: 28.11.1989, Medium: Taschenbuch, Einband: Kartoniert / Broschiert, Titel: The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Auflage: 1989, Autor: Hairer, Ernst // Lubich, Christian // Roche, Michel, Verlag: Springer Berlin Heidelberg // Springer Berlin, Sprache: Englisch, Rubrik: Mathematik // Analysis, Seiten: 156, Informationen: Paperback, Gewicht: 246 gr, Verkäufer: averdo

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Two implicit Hybrid block methods at step length k=2 and 3 were derived through collocation procedures. The two derived block methods also reconstructed to equivalent S stage Runge-Kutta type methods for the solution of y^'=f(x,y). Both methods were tested on the same numerical experiments. Runge-Kutta Type Methods (RKTM) gives better result over the equivalent linear multi-step methods of the same value of step length k.

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From the first time the author encountered General Linear Methods in general and Almost-Runge-Kutta methods in particular, and realized the enormous potentials and possibilities they provide, there has been a deep desire in the author, to draw the attention of researchers and mathematicians to these methods. As such, in this book the author has engaged in a detailed and comprehensive analysis of Almost Runge-Kutta (ARK) methods, derived new and effective methods especially for non-stiff differential equations. The book provides a comprehensive introduction to numerical methods for solving Ordinary Differential equations, it includes a detailed coverage of Runge-Kutta, linear multistep, and general linear methods,and thoroughly breaks down the derivation process of ARK methods. Extensive numerical experiments are carried out to see how the new ARK methods compare with some selected traditional methods and the results confirms the effectiveness and viability of ARK methods as a means by which Scientists, Mathematicians and Engineers can obtain accurate and reliable results for non-stiff differential equations.

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