# Equation methods

Xem 1-20 trên 211 kết quả Equation methods
• ### Numerical Methods for Ordinary Diﬀerential Equations

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 Runge-Kutta 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.

• ### Second-order ordinary differential equations

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).

• ### The Mathematical Theory of Maxwell’s Equations

Document "The Mathematical Theory of Maxwell’s Equations" give you the knowledge: The Variational Expansion into Wave Functions, Scattering From a Perfect Conductor, Approach to the Cavity Problem, Boundary Integral Equation Methods for Lipschitz Domains,...

• ### Finite Difference Methods in Financial Engineering

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 one-factor and multi-factor 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.

• ### Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods

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.

• ### Numerical Methods for Ordinary Differential Equations Butcher Tableau

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• ### Partial Differential Equation Toolbox

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.

• ### Implementing Models in Quantitative Finance: Methods and Cases

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, transform-based methods and quadrature techniques. Part II is practical, and features a number of self-contained cases.

• ### Numerical Methods for Nonlinear Variational Problems

Many mechanics and physics problems have variational formulations making them appropriate for numerical treatment by finite element techniques and efficient iterative methods. This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids.

• ### NUMERICAL METHODS AND MODELING FOR CHEMICAL ENGINEERS

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., diffusion-reaction, mass-heat 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....

• ### Deterministic Methods in Systems Hydrology

This work is intended to survey the basic theory that underlies the multitude of parameter-rich models that dominate the hydrological literature today. It is concerned with the application of the equation of continuity (which is the fundamental theorem of hydrology) in its complete form combined with a simplified representation of the principle of conservation of momentum. Since the equation of continuity can be expressed in linear form by a suitable choice of state variables and is also parameterfree, it can be readily formulated at all scales of interest.

• ### studies in surface science and catalysis METHODS FOR MONITORING AND DIAGNOSING THE

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• ### A Dressing Method in Mathematical Physics

The emergence of a new paradigm in science offers vast perspectives for future investigations, as well as providing fresh insight into existing areas of knowledge, discovering hitherto unknown relations between them. We can observe this kind of process in connection with the appearance of the concept of solitons [465].

• ### Introductory Finite Volume Methods for PDEs

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:

• ### Book: An introduction to partial differential equations

This text is intended to provide an introduction to the standard methods that are used for the solution of first-order partial differential equations. Some of these ideas are likely to be introduced, probably in a course on mathematical methods during the second year of a degree programme with, perhaps, more detail in a third year. The material has been written to provide a general – but broad – introduction to the relevant ideas, and not as a text closely linked to a specific module or course of study. Indeed, the intention is to present the material so that it can be used as an...

• ### Second-order ordinary differential equations Special functions, Sturm-Liouville theory and transforms

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 Sturm-Liouville 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).

• ### Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject was still fairly novel. Motivated by the many favorable comments we have received and the continuing interest in that book (which will be referred to as CHQZ1), and yet desiring to present a more modern perspective, we embarked on the project which resulted in our recent book (Canuto et al. (2006), referred to as CHQZ2) and the present new book (referred to as CHQZ3).

• ### Computational Methods in Plasma Physics

What is computational physics? Here, we take it to mean techniques for simulating continuous physical systems on computers. Since mathematical physics expresses these systems as partial differential equations, an equivalent statement is that computational physics involves solving systems of partial differential equations on a computer. This book is meant to provide an introduction to computational physics to students in plasma physics and related disciplines. We present most of the basic concepts needed for numerical solution of partial differential equations.

• ### Examples of Applications of The Power Series Method By Solution of Differential Equations with Polynomial Coefﬁcients Calculus 3c-4

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