Introduction to computation and modeling for differential equations / / Lennart Edsberg

• Record Nr.: UNINA9910460739403321
• Autore: Edsberg Lennart <1946->
• Pubbl/distr/stampa: Hoboken, New Jersey : , : Wiley, , 2016; ©2016
• ISBN: 1-119-01846-3; 1-119-01845-5
• Edizione: [Second edition.]
• Descrizione fisica: 1 online resource (328 p.)
• Disciplina: 515/.350285
• Soggetti: Differential equations - Data processing; Mathematical models; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: ""Title Page""; ""Copyright""; ""Table of Contents""; ""Preface""; ""Chapter 1: Introduction""; ""1.1 What is a Differential Equation?""; ""1.2 Examples of an ordinary and a partial differential equation""; ""1.3 Numerical analysis, a necessity for scientific computing""; ""1.4 Outline of the contents of this book""; ""Bibliography""; ""Chapter 2: Ordinary Differential Equations""; ""2.1 Problem Classification""; ""2.2 Linear Systems of Odes With Constant Coefficients""; ""2.3 Some Stability Concepts For Ode""; ""2.4 Some ode models in science and engineering""; ""2.5 Some Examples From Applications""""Bibliography""; ""Chapter 3: Numerical Methods For Initial Value Problems""; ""3.1 Graphical Representation Of Solutions""; ""3.2 Basic Principles Of Numerical Approximation Of ODE""; ""3.3 Numerical Solution Of IVP with euler' method""; ""3.4 Higher order methods for the IVP""; ""3.5 Special Methods For Special Problems""; ""3.6 The Variational Equation And Parameter Fitting In IVP""; ""Bibliography""; ""Chapter 4: Numerical methods for boundary value problems""; ""4.1 Applications""; ""4.2 Difference methods for BVP""; ""4.3 Ansatz methods for BVP""; ""Bibliography""""Chapter 5: Partial differential equations""; ""5.1 Classical PDE problems""; ""5.2 Differential operators used for PDEs""; ""5.3 Some PDE in science and engineering""; ""5.4 Initial and boundary conditions for PDE""; ""5.5 Numerical solution of PDEs, some general comments""; ""Bibliography""; ""Chapter 6: Numerical Methods for Parabolic Partial Differential Equations""; ""6.1 Applications""; ""6.2 An introductory example of discretization""; ""6.3 THE METHOD OF LINES FOR PARABOLIC PDEs""; ""6.4 Generalizations of the heat equation""; ""6.5 Ansatz methods for the model equation""""Bibliography""; ""Chapter 7: Numerical methods for elliptic partial differential equations""; ""7.1 Applications""; ""7.2 The finite difference method""; ""7.3 Discretization of a problem with different BCs""; ""7.4 ANSATZ Methods For Elliptic PDE""; ""Bibliography""; ""Chapter 8: Numerical methods for hyperbolic PDE""; ""8.1 Applications""; ""8.2 Numerical solution of hyperbolic PDE""; ""8.3 The Finite Volume Method""; ""8.4 Some examples of stability analysis for hyperbolic PDE""; ""Bibliography""; ""Chapter 9: Mathematical Modeling with Differential Equations""""9.1 NATURE LAWS""; ""9.2 CONSTITUTIVE EQUATIONS""; ""9.3 CONSERVATIVE EQUATIONS""; ""9.4 SCALING OF DIFFERENTIAL EQUATIONS TO DIMENSIONLESS FORM""; ""Chapter 10: Applied Projects On Differential Equations""; ""Appendix A: Some Numerical and Mathematical Tools""; ""A.1 Newton's Method for Systems of Nonlinear Algebraic Equations""; ""A.2 Some Facts about Linear Difference Equations""; ""A.3 Derivation of Difference Approximations""; ""Bibliography""; ""A.4 THE INTERPRETATIONS OF GRAD, DIV, AND CURL""; ""A.5 NUMERICAL SOLUTION OF ALGEBRAIC SYSTEMS OF EQUATIONS""