79,90 € *

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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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79,90 € *

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67,99 € *

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Numerical Methods for Non-Stiff Differential Equations ab 67.99 € als Taschenbuch: Almost Runge-Kutta (ARK) Methods. Aus dem Bereich: Bücher, Wissenschaft, Mathematik,

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49,00 € *

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The book has three chapters and an Appendix on different methods to calculate approximate areas of plain regions enclosed by curves. Tutorials, Tests and Examination Papers of different Universities where the author taught the course at the faculties of Engineering and Business Studies are provided. A short bibliography of books on the subject and alphabetical index of the topics covered are given in the end.The first chapter accounts the different methods for numerical solutions of ordinary differential equations. Picard's, Taylor's, Euler's, Runge-Kutta, Milne's and Adams-Bashforth's methods are given. The problems of curve fittings and spline fittings are explained in the second chapter. The Gaussian method of least squares' for the curve of best fit' is included. The concepts of Linear Programming are studied in the third chapter. Solution(s) of linear relations obtained analytically are also discussed by graphical methods. General problems of Linear Programming (LPP), canonical and standard forms of LPP and Simplex methods are discussed. Trapezoidal rule and Simpson's rules for approximate areas of plain regions are included in the Appendix

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The main contribution of this work is illustrated as follows: 1- The derivation for embedded singly diagonally implicit Runge-Kutta (SDIRK) method of fourth-order six stages in fifth-order seven stages is introduced to solve ordinary and delay differential equations. The stability region is presented and the numerical results are compared with the other existing methods. 2- Singly diagonally implicit Runge-Kutta Nystróm (SDIRKN) of third-order three stages embedded in fourth-order four stages is constructed. The stability region of the new method is presented and numerical results are compared with the same method of lower order. 3- A new singly diagonally implicit Runge-Kutta-Nystróm general (SDIRKNG) method of third-order embedded in fourth-order is derived to solve second order ordinary differential equations. Analysis the stability region of the new method is discussed and numerical results are presented.

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The numerical approximation of solutions of ordinarydifferential equations played an important role inNumerical Analysis and still continues to be anactive field of research. In this book we are mainlyconcerned with the numerical solution of thefirst-order system of nonlinear two-point boundaryvalue problems. We will focus on the problem ofsolving singular perturbation problems since this hasfor many years been a source of difficulty to appliedmathematicians, engineers and numerical analystsalike. Firstly, we consider deferred correctionschemes based on Mono-Implicit Runge-Kutta (MIRK) andLobatto formulae. As is to be expected, the schemebased on Lobatto formulae, which are implicit, ismore stable than the scheme based on MIRK formulaewhich are explicit. Secondly, we construct high orderinterpolants to provide the continuous extension ofthe discrete solution. It will consider theconstruction of both explicit and implicitinterpolants. The estimation of conditioning numbersis also discussed and used to develop mesh selectionalgorithms which will be appropriate for solvingstiff linear and nonlinear boundary value problems.

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59,00 € *

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The gas-kinetic methods for viscous flow simulations have attracted much attention and become mature during the past decade. Ever since they were originally invented for compressible gas flows, the gas-kinetic methods have been extended to various viscous flow problems with a large number of applications. This book not only provides an introduction to the gas-kinetic methods, but also presents some recent progress on these useful and powerful methods. Besides the original gas-kinetic finite volume scheme for the Euler and Navier-Stokes equations, the book also covers in detail the following extensions of the method: the high order gas-kinetic Runge-Kutta discontinuous Galerkin finite element method for Navier-Stokes equations, the multiscale gas-kinetic method for flows in near continuum regime including rarefied gas and microscale gas flows, the multiple temperature kinetic model for microscale flow problems. Plenty of numerical examples are exhibited to validate these methods. The book addresses researchers as well as graduate students and engineers interested in learning, using, or further developing the gas-kinetic methods.

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The 5-moment two-fluid plasma model uses Euler equations to describe the ion and electron fluids, and Maxwell's equations to describe the electric and magnetic fields. Two-fluid physics becomes significant when the characteristic spatial scales are on the order of the ion skin depth and characteristic time scales are on the order of the inverse ion cyclotron frequency. The two-fluid plasma model has disparate characteristic speeds ranging from the ion and electron speeds of sound to the speed of light. Explicit and implicit time-stepping schemes are explored for the two-fluid plasma model to study the accuracy and computational effectiveness with which they could capture two-fluid physics. The explicit schemes explored include the high resolution wave propagation method (a finite volume method) and the Runge-Kutta discontinuous Galerkin method (a finite element method). The two-fluid plasma model is compared to the more commonly used Hall-MHD model for accuracy and computational effort using an explicit time-stepping scheme. Simulations of two-fluid instabilities in the Z-pinch and the field-reversed configuration are presented in 3-dimensions.

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61,90 € *

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A numerical analysis was performed as to investigate the heat transfer characteristics of an evaporating thin-film meniscus. A mathematical model was used in the formulation of a third order ordinary differential equation. This equation governs the evaporating thinfilm through use of continuity, momentum, energy equations and the Kelvin-Clapeyron model. This governing equation was treated as an initial value problem and was solved numerically using a Runge-Kutta technique. The numerical model uses varying thermophysical properties and boundary conditions such as channel width, applied superheat, accommodation coefficient and working fluid which can be tailored by the user. This work focused mainly on the effects of altering accommodation coefficient and applied superheat. A unified solution is also presented which models the meniscus to half channel width. The model was validated through comparison to literature values.

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