Villadsen J., Michelsen M.L. Solution of Differential Equation Models by Polynomial Approximation

Cengage Learning, 2001, 850 pp. , 7 edition. Mathematical preliminaries. solutions of equations in one variable. interpolation and polynomial approximation. numerical differentiation and integration. initial-Value problems for ordinary differential equations. direct methods for solving linear systems. iterative techniques in matrix algebra. approximation theory. approximating eigenvalues. numerical solutions of nonlinear systems of equations. bou...

George W. Collins, II, 2003. - 284 pages. * Contents and Introduction * Chapter 1: Introduction and Fundamental Concepts * Chapter 2: The Numerical Methods for Linear Equations and Matrices * Chapter 3: Polynomial Approximation, Interpolation, and Orthogonal Polynomials * Chapter 4: Numerical Evaluation of Derivatives and Integrals * Chapter 5: Numerical Solution of Differential and Integral Equations * Chapter 6: Least Squares, Fourier An...

Birkh?user Boston, 2005. - 329 pages. The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations. An essential step in such investigations is the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained...

Springer, 1992. - 305 Pages. This book is a basic and comprehensive introduction to the use of spectral methods for the approximation of the solution to ordinary differential equations and time-dependent boundary-value problems. The algorithms are presented and studied both from the point of view of the theoreticalanalysis of convergence and the numerical implementation. Unlike other texts devoted to the subject this is a concise introduction th...

Springer, 2011. - 538 pages. This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) descri...

Elsevier Inc, 2011. - 445 pages. Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, p...

Springer, 2010. - 614 pages. The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergenc...

CRC, 1998. - 384 pages. Matrix Algebra and Solution of Matrix Equations. Introduction. Manipulation of Matrices. Solution of Matrix Equation. Program Gauss — Gaussian Elimination Method. Matrix Inversion, Determinant, and Program MatxInvD. Problems. Reference. Exact, Least-Squares, and Spline Curve-Fits. Introduction. Exact Curve Fit. Program LeastSq1 — Linear Least-Squares Curve-Fit. Program LeastSqG — Generalized Least-Squares Curve-Fit. Progr...

Sрringеr, 2008. - 284 pages. The book presents fundamental numerical methods which are most frequently applied in the electrical (electronic) engineering. A scope of this book is rather wide and includes solving the sets of linear and nonlinear equations, interpolation and approximation of the functions of one variable, integration and differentation of the functions of one and two variables, integration of the ordinary differential equations, a...

Cambridge University, 2009. - 490 Pages. A Compendium of Partial Differential Equation Models presents numerical methods and associated computer codes in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs), one of the mostly widely used forms of mathematics in science and engineering. The authors focus on the method of lines (MOL), a well-established numerical procedure for all major classes of PDEs...