Numerical methods for nonlinear engineering models / John R. Hauser

Auteur secondaire : Hauser, John R. - Editeur scientifiqueType de document: Livre numériqueLangue: anglaisÉditeur: Dordrecht : Springer, 2009 ISBN: 9781402099205 Note: The book represents a comprehensive guide for the exploitation of standard numerical tools in nonlinear engineering problems. The presentation style ensures a balanced construction in providing mathematical knowledge illustrated by relevant examples. The material is organized in the following chapters: 1. Introduction to nonlinear engineering problems and models; 2. Numerical fundamentals and computer programming; 3. Roots of nonlinear equations; 4. Solving sets of equations: linear and nonlinear; 5. Numerical derivatives and numerical integration; 6. Interpolation; 7. Curve fitting and data plotting; 8. Statistical methods and basic statistical functions; 9. Data models and parameter estimation; 10. Differential equations: initial value problems; 11. Differential equations: boundary value problems; 12. Partial differential equations: finite difference approaches; 13. Partial differential equations: the finite element method. All these topics are accompanied by computer codes developed in the Lua programming language. An appendix of the main text offers a shortened form of the Lua Reference Manual. The software supplied by the book is available on a CD. The arrangement of the material makes it equally suitable for self-study and teaching support at the first postgraduate level. The book is recommended to educators interested in preparing or upgrading lecture notes and seminars, students specializing in different fields of engineering, and practitioners working with various types of nonlinear models. (zbMath) Sujets MSC: 65Dxx Numerical analysis -- Numerical approximation and computational geometry (primarily algorithms)
65Hxx Numerical analysis -- Nonlinear algebraic or transcendental equations
65Lxx Numerical analysis -- Ordinary differential equations
65Mxx Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems
00A06 General -- General and miscellaneous specific topics -- Mathematics for nonmathematicians (engineering, social sciences, etc.)
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The book represents a comprehensive guide for the exploitation of standard numerical tools in nonlinear engineering problems. The presentation style ensures a balanced construction in providing mathematical knowledge illustrated by relevant examples.

The material is organized in the following chapters: 1. Introduction to nonlinear engineering problems and models; 2. Numerical fundamentals and computer programming; 3. Roots of nonlinear equations; 4. Solving sets of equations: linear and nonlinear; 5. Numerical derivatives and numerical integration; 6. Interpolation; 7. Curve fitting and data plotting; 8. Statistical methods and basic statistical functions; 9. Data models and parameter estimation; 10. Differential equations: initial value problems; 11. Differential equations: boundary value problems; 12. Partial differential equations: finite difference approaches; 13. Partial differential equations: the finite element method.

All these topics are accompanied by computer codes developed in the Lua programming language. An appendix of the main text offers a shortened form of the Lua Reference Manual. The software supplied by the book is available on a CD. The arrangement of the material makes it equally suitable for self-study and teaching support at the first postgraduate level. The book is recommended to educators interested in preparing or upgrading lecture notes and seminars, students specializing in different fields of engineering, and practitioners working with various types of nonlinear models. (zbMath)

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