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This book presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $bar{delta}$-method. Exercises are included throughout, which makes this text ideal for a one- or two-semester graduate course.This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L² -method, a powerful technique used in the theory of several complex variables. The work features a simple construction of a strictly subharmonic exhaustion function and a related construction of a positive-curvature Hermitian metric in a holomorphic line bundle, topics which serve as starting points for proofs of standard results such as the Mittag-Leffler, Weierstrass, and Runge theorems; the Riemann Roch theorem; the Serre duality and Hodge decomposition theorems; and the uniformization theorem. The book also contains treatments of other facts concerning the holomorphic, smooth, and topological structure of a Riemann surface, such as the biholomorphic classification of Riemann surfaces, the embedding theorems, the integrability of almost complex structures, the Schönflies theorem (and the Jordan curve theorem), and the existence of smooth structures on second countable surfaces. Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the only prerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercises many of which lead to further development of the theory and presents (with proofs) streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester graduate course. Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the only prerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercises many of which lead to further development of the theory and presents (with proofs) streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester graduate course. Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the only prerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercises many of which lead to further development of the theory and presents (with proofs) streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester graduate course.

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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 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.

Anbieter: Dodax

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Majority of the current numerical simulation methods for time-dependent flows are limited to second order accuracy in time discretization. Moreover, usual simulation methods rely on explicit time discretization methods for which numerical stability of solution is generally guaranteed only with very small time step sizes. Major commercial CFD software programs provide options for implicit time advancing, but the accuracy is limited to second order in time. In this book a stable simulation method is proposed that can be used to achieve arbitrarily high order of accuracy in time advancement in simulation of time-dependent flows and heat transfer. The strategy is to combine the state-of-the-art mathematical tools with proven flow simulation algorithms to develop simulation techniques with higher-order accuracy. A special class of implicit Runge-Kutta methods is used in conjunction with SIMPLE algorithm. The proposed method is called SIMPLE DIRK method. This book will be helpful to university students and researchers who are involved in research and code development for simulation of time-dependent flows and heat transfer.

Anbieter: Dodax

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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 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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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The finite element method (FEM) (its practical application often known as finite element analysis (FEA)) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler''s method, Runge-Kutta, etc.

Anbieter: Dodax

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The book deals with the basic concepts of fluid dynamics and heat, mass transfer behavior of Newtonian and non-Newtonian fluid past an extending surfaces. The considered subject is perceived by the researchers and post-doctoral researchers. In this book we introduces computational numerical tool for solving highly non-linear differential equations models that arise in flow of fluid, heat and mass transfer of both Newtonian/non-Newtonian fluid problem. Self similar solutions are obtained using the fourth-fifth order Runge-Kutta-Fehlberg method. The considered work has great importance in the field of science and technology. The considered problem is quite useful in guided missiles, rain erosion, uidization, atmospheric fallout, paint and aerosol spraying,lunar ash ows,and cooling of nuclear reactor.

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The purpose of this work is to determinate the approximate solutions of boundary value problems with conditions inside the interval (0,1) using collocation method with global B-splines functions of degree k(order k+1), orthogonal polynomials Chebyshev and combined methods with B-splines functions or C.C method and Runge-Kutta methods. We do a comparative study of these numerical methods, making their implementation of algorithms written in MATLAB 2011b, Maple 2014 and we was also concerned with the approximations errors and determine their implementations costs (run time and internal memory used).

Anbieter: Dodax

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