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Erscheinungsdatum: 01/2011, Medium: Taschenbuch, Einband: Kartoniert / Broschiert, Titel: Numerical Methods for Non-Stiff Differential Equations, Titelzusatz: Almost Runge-Kutta (ARK) Methods, Autor: ABRAHAM, OCHOCHE, Verlag: LAP Lambert Acad. Publ., Sprache: Englisch, Rubrik: Mathematik // Sonstiges, Seiten: 196, Informationen: Paperback, Gewicht: 308 gr, Verkäufer: averdo

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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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26,49 € *

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The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods ab 26.49 € als Taschenbuch: Auflage 1989. Aus dem Bereich: Bücher, Wissenschaft, Mathematik,

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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. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.

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26,49 € *

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The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods ab 26.49 EURO Auflage 1989

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The monograph presents a new approach to modeling and studying dynamic processes in the simplest two-link systems, where the input and output connections are somehow connected or interact with each other. It is shown that, neglecting nonlinearities, these systems can be described by analogous differential equations. The new method explicitly takes into account fluctuations in the speed of movement and tension. Using the Laplace transformations allowed us to derive equations describing the dynamics in a more general form. In this case, the elasticity of the system was considered as a function depending, in addition to the line parameters, on the oscillation frequency, which under certain conditions may lead to loss of stability. The theory of stability of open-loop systems with distributed parameters is obtained. For the cases of using internal feedbacks on the intermediate coordinate (pressure, voltage), a new frequency method for estimating stability was developed. The book contains new numerical methods based on the Runge-Kutta method, which made it possible to accurately simulate dynamic processes in nonlinear systems with lumped and distributed parameters.

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35,90 € *

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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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49,90 € *

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This research presents numerical solution of Whitham-Broer-Kaup (WBK) shallow water model using some finite difference methods such as the explicit, implicit, Crank-Nicolson, exponential, Richardson, and DuFort-Frankel methods. The local truncation errors and consistency are also studied for these methods. Furthermore, the radial basis function-pseudospectral method is successfully applied for solving WBK model numerically. In this method, the model is discretized in the space x which leads to a system of ordinary differential equations with independent variable time t. Then the forward Euler's and fourth-order Runge-Kutta methods used to solve this system of ordinary differential equations. Finally, two different problems are considered to illustrate the efficiency of the methods. A comparative study is made between the approximate solution obtained by the presented numerical methods and the exact solution. The MATLAB codes have been written for all methods as can be found in the appendix.

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