Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB

H.J. Lee, W.E. Schiesser

519 pages, parution le 05/01/2004

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Résumé

Describes the first-ever implementation of a major ODE/PDE library in JAVA
Reviews the basic concepts of numerical integration
Includes source code for all six languages covered
Provides fixed step and variable step integrators that are capable of solving a broad spectrum of ODE and PDE problems
Discusses truncation error monitoring and control, h and p refinement, stability and stiffness, and explicit and implicit algorithms, as they relate to ODE/PDE integration
Demonstrates extensions to stiff systems via an ODE application
Illustrates the application of ODE integration routines to PDEs through the method of lines
(MOL).

Scientists and engineers attempting to solve complex problems require efficient, effective ways of applying numerical methods to ODEs and PDEs. They need a resource that enables fast access to library routines in their choice of a programming language.

Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB provides a set of ODE/PDE integration routines in the six most widely used languages in science and engineering, enabling scientists and engineers to apply ODE/PDE analysis toward solving complex problems.

This text concisely reviews integration algorithms, then analyzes the widely used Runge Kutta method ( since hyphenation is used here, I added it below; hyphenation could also be dropped since it is not used in the book). It first presents a complete code before discussing its components in detail, focusing on integration concepts such as error monitoring and control.

The format allows you to understand the basics of ODE/PDE integration, then calculate sample numerical solutions within your targeted programming language. The applications discussed can be used as templates for the development of a spectrum of new applications and associated codes.

L'auteur - H.J. Lee

Arizona State University, Tempe, USA

L'auteur - W.E. Schiesser

Lehigh University, Bethlehem, Pennsylvania, USA

Sommaire

Some basics of ODE integration
- General Initial Value ODE Problem
- Origin of ODE Integrators in the Taylor Series
- The Runge-Kutta Method
- Accuracy of RK Methods
- Embedded RK Algorithms
- Library ODE Integrators
- Stability of RK Methods
Solution of a 1 x 1 ODE system
- Programming in MATLAB
- Programming in C
- Programming in C++
- Programming in FORTRAN (all CAPs?)
- Programming in Java
- Programming in Maple
Solution of a 2 x 2 ODE system
- Programming in MATLAB
- Programming in C
- Programming in C++
- Programming in FORTRAN
- Programming in Java
- Programming in Maple
Solution of a linear PDE
- Programming in MATLAB
- Programming in C
- Programming in C++
- Programming in FORTRAN
- Programming in Java
- Programming in Maple
Solution of a nonlinear PDE
- Programming in MATLAB
- Programming in C
- Programming in C++
- Programming in FORTRAN
- Programming in Java
- Programming in Maple
Appendices
- Embedded Runge-Kutta Pairs
- Integrals from ODEs
- Stiff ODE Integration (title was changed)
- Alternate Forms of ODEs
- Spatial p Refinement
- Testing ODE/PDE Codes

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	H.J. Lee, W.E. Schiesser
Parution	05/01/2004
Nb. de pages	519
Format	16 x 24
Couverture	Relié
Poids	835g
Intérieur	Noir et Blanc
EAN13	9781584884231
ISBN13	978-1-58488-423-1