Integration Of Equations Of Parabolic Type By The Method Of Nets
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Integration Of Equations Of Parabolic Type By The Method Of Nets
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Author : V. K. Saul'Yev
language : en
Publisher: Elsevier
Release Date : 2014-07-10
Integration Of Equations Of Parabolic Type By The Method Of Nets written by V. K. Saul'Yev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
International Series of Monographs in Pure and Applied Mathematics, Volume 54: Integration of Equations of Parabolic Type by the Method of Nets deals with solving parabolic partial differential equations using the method of nets. The first part of this volume focuses on the construction of net equations, with emphasis on the stability and accuracy of the approximating net equations. The method of nets or method of finite differences (used to define the corresponding numerical method in ordinary differential equations) is one of many different approximate methods of integration of partial differential equations. The other methods, and some based on newer equations, are described. By analyzing these newer methods, older and existing methods are evaluated. For example, the asymmetric net equations; the alternating method of using certain equations; and the method of mean arithmetic and multi-nodal symmetric method point out that when the accuracy needs to be high, the requirements for stability become more defined. The methods discussed are very theoretical and methodological. The second part of the book concerns the practical numerical solution of the equations posed in Part I. Emphasis is on the commonly used iterative methods that are programmable on computers. This book is suitable for statisticians and numerical analysts and is also recommended for scientists and engineers with general mathematical knowledge.
Integration Of Equations Of Parabolic Type By The Method Of Nets
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Author : Vladislav Klimentʹevič Saulʹev
language : en
Publisher:
Release Date : 1964
Integration Of Equations Of Parabolic Type By The Method Of Nets written by Vladislav Klimentʹevič Saulʹev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Convergence categories.
Integration Of Equations Of Parabolic Type By The Method Of Nets
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Author : Vladislav Klimentʹevich Saulʹev
language : en
Publisher:
Release Date : 1964
Integration Of Equations Of Parabolic Type By The Method Of Nets written by Vladislav Klimentʹevich Saulʹev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Differential equations, Partial categories.
Integration Of Equations Of Parabolic Type By The Method Of Nets
DOWNLOAD
Author : V. K. Saul'yev
language : en
Publisher:
Release Date : 1964
Integration Of Equations Of Parabolic Type By The Method Of Nets written by V. K. Saul'yev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Differential equations, Partial categories.
Integration Of Equations Of Parabolic Type By The Method Of Nets
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Author : Doris Lessing
language : en
Publisher:
Release Date : 1964
Integration Of Equations Of Parabolic Type By The Method Of Nets written by Doris Lessing and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
Block Method For Solving The Laplace Equation And For Constructing Conformal Mappings
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Author : Evgenii A. Volkov
language : en
Publisher: CRC Press
Release Date : 2017-07-28
Block Method For Solving The Laplace Equation And For Constructing Conformal Mappings written by Evgenii A. Volkov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-28 with Mathematics categories.
This book presents a new, efficient numerical-analytical method for solving the Laplace equation on an arbitrary polygon. This method, called the approximate block method, overcomes indicated difficulties and has qualitatively more rapid convergence than well-known difference and variational-difference methods. The block method also solves the complicated problem of approximate conformal mapping of multiply-connected polygons onto canonical domains with no preliminary information required. The high-precision results of calculations carried out on the computer are presented in an abundance of tables substantiating the exponential convergence of the block method and its strong stability concerning the rounding-off of errors.
The Method Of Summary Representation For Numerical Solution Of Problems Of Mathematical Physics
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Author : G. N. Polozhii
language : en
Publisher: Elsevier
Release Date : 2014-07-10
The Method Of Summary Representation For Numerical Solution Of Problems Of Mathematical Physics written by G. N. Polozhii and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
Pure and Applied Mathematics, Volume 79: The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics presents the numerical solution of two-dimensional and three-dimensional boundary-value problems of mathematical physics. This book focuses on the second-order and fourth-order linear differential equations. Organized into two chapters, this volume begins with an overview of ordinary finite-difference equations and the general solutions of certain specific finite-difference equations. This text then examines the various methods of successive approximation that are used exclusively for solving finite-difference equations. This book discusses as well the established formula of summary representation for certain finite-difference operators that are associated with partial differential equations of mathematical physics. The final chapter deals with the formula of summary representation to enable the researcher to write the solution of the corresponding systems of linear algebraic equations in a simple form. This book is a valuable resource for mathematicians and physicists.
Finite Difference Methods In Financial Engineering
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Author : Daniel J. Duffy
language : en
Publisher: John Wiley & Sons
Release Date : 2013-10-28
Finite Difference Methods In Financial Engineering written by Daniel J. Duffy and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-28 with Business & Economics categories.
The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.
Numerical Methods For Partial Differential Equations
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Author : William F. Ames
language : en
Publisher: Academic Press
Release Date : 2014-06-28
Numerical Methods For Partial Differential Equations written by William F. Ames and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses
A Collection Of Problems On A Course Of Mathematical Analysis
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Author : G. N. Berman
language : en
Publisher: Elsevier
Release Date : 2016-06-06
A Collection Of Problems On A Course Of Mathematical Analysis written by G. N. Berman and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-06 with Mathematics categories.
A Collection of Problems on a Course of Mathematical Analysis is a collection of systematically selected problems and exercises (with corresponding solutions) in mathematical analysis. A common instruction precedes a group of problems of the same type. Problems with a physics content are preceded by the necessary physical laws. In the case of more or less difficult problems, hints are given in the answers. This book is comprised of 15 chapters and begins with an overview of functions and methods of specifying them; notation for and classification of functions; elementary investigation of functions; and trigonometric and inverse trigonometric functions. The following chapters deal with limits and tests for their existence; differential calculus, with emphasis on derivatives and differentials; functions and curves; definite and indefinite integrals; and methods of evaluating definite integrals. Some applications of the integral in geometry, statics, and physics are also considered; along with functions of several variables; multiple integrals and iterated integration; line and surface integrals; and differential equations. The final chapter is devoted to trigonometric series. This monograph is intended for students studying mathematical analysis within the framework of a technical college course.