Differential method

The goal of this book is to develop robust, accurate and efficient numerical methods to price a number of derivative products in quantitative finance.We focus on onefactor and multifactor models for a wide range of derivative products such as options, fixed income products, interest rate products and ‘real’ options. Due to the complexity of these products it is very difficult to find exact or closed solutions for the pricing functions. Even if a closed solution can be found it may be very difficult to compute. For this and other reasons we need to resort to approximate methods.
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Computational fluid dynamics (CFD) is concerned with the efficient numerical solution of the partial differential equations that describe fluid dynamics. CFD techniques are commonly used in the many areas of engineering where fluid behavior is an important factor. Traditional fields of application include aerospace and automotive design, and more recently, bioengineering and consumer and medical electronics.
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Tham khảo sách 'numerical methods for ordinary differential equations butcher tableau', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả
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This section attempts to answer some of the questions you might formulate when you turn the first page: What does this toolbox do? Can I use it? What problems can I solve?, etc. What Does this Toolbox Do? The Partial Differential Equation (PDE) Toolbox provides a powerful and flexible environment for the study and solution of partial differential equations in two space dimensions and time. The equations are discretized by the Finite Element Method (FEM). The objectives of the PDE Toolbox are to provide you with tools that: • Define a PDE problem, i.e.
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This book presents and develops major numerical methods currently used for solving problems arising in quantitative finance. Our presentation splits into two parts. Part I is methodological, and offers a comprehensive toolkit on numerical methods and algorithms. This includes Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula functions, transformbased methods and quadrature techniques. Part II is practical, and features a number of selfcontained cases.
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In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on RungeKutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding.
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This volume is an eclectic mix of applications of Monte Carlo methods in many fields of research should not be surprising, because of the ubiquitous use of these methods in many fields of human endeavor. In an attempt to focus attention on a manageable set of applications, the main thrust of this book is to emphasize applications of Monte Carlo simulation methods in biology and medicine.
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The goal of this book is to expose the reader to modern computational tools for solving differential equation models that arise in chemical engineering, e.g., diffusionreaction, massheat transfer, and fluid flow. The emphasis is placed on the understanding and proper use of software packages. In each chapter we outline numerical techniques that either illustrate a computational property of interest or are the underlying methods of a computer package. At the close of each chapter a survey of computer packages is accompanied by examples of their use....
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This material is taught in the BSc. Mathematics degree programme at the Manchester Metropolitan University, UK. The Finite Volume Method (FVM) is taught after the Finite Difference Method (FDM) where important concepts such as convergence, consistency and stability are presented. The FDM material is contained in the online textbook, ‘Introductory Finite Difference Methods for PDEs’ which is free to download from:
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The three texts in this one cover, entitled ‘The series solution of second order, ordinary differential equations and special functions’ (Part I), ‘An introduction to SturmLiouville theory’ (Part II) and ‘Integral transforms’ (Part III), are three of the ‘Notebook’ series available as additional and background reading to students at Newcastle University (UK).
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Differential evolution is one of the most recent global optimizers. Discovered in 1995 it rapidly proved its practical efficiency. This book gives you a chance to learn all about differential evolution. On reading it you will be able to profitably apply this reliable method to problems in your field. As for me, my passion for intelligent systems and optimization began as far back as during my studies at Moscow State Technical University of Bauman, the best engineering school in Russia. At that time, I was gathering material for my future thesis.
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n mathematics, an ordinary differential equation (abbreviated ODE) is an equation containing a function of one independent variable and its derivatives. There are many general forms an ODE can take, and these are classified in practice (see below).[1][2] The derivatives are ordinary because partial derivatives only apply to functions of many independent variables (see Partial differential equation).
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The present volume, compiled in honor of an outstanding historian of science, physicist and exceptional human being, Sam Schweber, is unique in assembling a broad spectrum of positions on the history of science by some of its leading representatives. Readers will find it illuminating to learn how prominent authors judge the current status and the future perspectives of their field. Students will find this volume helpful as a guide in a fragmented field that continues to be dominated by idiosyncratic expertise and still lacks a methodical canon.
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This note deals with two fully parallel methods for solving linear partial differentialalgebraic equations (PDAEs) of the form: Aut + B∆u = f(x, t) where A is a singular, symmetric and nonnegative matrix, while B is a symmetric positive define matrix. The stability and convergence of proposed methods are discussed. Some numerical experiments on highperformance computers are also reported.
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We have attempted to write a concise modern treatment of differential equations emphasizing applications and containing all the core parts of a course in differential equations.Asemester or quarter course in differential equations is taught to most engineering students (and many science students) at all universities, usually in the second year. Some universities have an earlier brief introduction to differential equations and others do not. Some students will have already seen some differential equations in their science classes.We do not assume any prior exposure to differential equations.
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Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "realworld" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation.
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The fifth edition of this classic book continues its excellence in teaching numerical analysis and techniques. Interesting and timely applications motivate an understanding of methods and analysis of results. Suitable for students with mathematics and engineering backgrounds, the breadth of topics (partial differential equations, systems of nonlinear equations, and matrix algebra), provide comprehensive and flexible coverage of all aspects of all numerical analysis.
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The principle of Occam’s razor loosely translates to “the simplest solution is often the best”. The author of Kinematic Geometry of Surface Machining utilizes this reductionist philosophy to provide a solution to the highly inefficient process of machining sculptured parts on multiaxis NC machines. He has developed a method to quickly calculate the necessary parameters, greatly reduce trial and error, and achieve efficient machining processes by using less input information, and in turn saving a great deal of time.
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In addition to Excel's extensive list of worksheet functions and array of calculation tools for scientific and engineering calculations, Excel contains a programming language that allows users to create procedures, sometimes referred to as macros, that can perform even more advanced calculations or that can automate repetitive calculations.
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