Numerical methods for differential equations : fundamental concepts for scientific and engineering applications
著者
書誌事項
Numerical methods for differential equations : fundamental concepts for scientific and engineering applications
Prentice Hall, c1992
大学図書館所蔵 全10件
注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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