Numerical methods for differential equations : fundamental concepts for scientific and engineering applications
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Bibliographic Information
Numerical methods for differential equations : fundamental concepts for scientific and engineering applications
Prentice Hall, c1992
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Includes bibliographical references and index
Description and Table of Contents
Description
Senior/Graduate level text covering numerical methods used to solve ordinary and partial differential equations in science and engineering. Emphasis is on problem-solving as a means of gaining a deeper understanding of the fundamental concepts. Not a cookbook of formulas. Topics include an introduction to partial differential equations, finite difference method, finite element approximations, design of numerical approximations, and analytical tools. Includes review of linear algebra.
Table of Contents
- Part 1 Introduction to partial differential equations: behaviour physical systems
- definitions and equation properties
- conclusion
- problems. Part 2 Finite difference methods: discrete approximations in one dimension
- a generalized formulation of differences
- example calculations in one dimension
- solution of initial value problems finite differences
- multiple dimension
- two-dimensional example calculations
- conclusion
- problems. Part 3 Finite element methods: the methods of weighted residuals
- nomenclature
- computational procedures in one dimension
- mathematical requirements
- method of weighted residuals in two dimensions
- method of weighted residuals in three dimensions
- mathematical properties of the Galerkin finite element method
- conclusion. Part 4 Discretization considerations and design of approximations: spatial discretization
- temporal discretization
- space-time discretization
- alternative numerical procedures
- conclusion
- problems. Part 5 Accuracy and error reduction: improved accuracy through Mesh refinement
- improved accuracy through higher order approximation
- considerations of space-time problems
- conclusion
- problems.
by "Nielsen BookData"