Neta B. Numerical Solution of Partial Differential Equations: Solutions of Problems in Lecture Notes

Academic Press, 1992. - 433 pages. This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Pa...

Mathematics in Science and Engineering, Volume 88. Academic Press, 1972. 204 pages. A major task of contemporary mathematical analysis is that of providing computer algorithms for the numerical solution of partial differential equations of all types. This task requires a motley mixture of methods. In this book we wish to show first that dynamic programming and invariant imbedding furnish some powerful techniques for the solution of linear elli...

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...

Wiley-Interscience, 1999. - 677 pages. Incorporates the essential elements of all the numerical methods currently used in the solution of partial differential equations encountered in science and engineering. Considers partial differential equations by their type (parabolic, elliptic, or hyperbolic), and applies all relevant numerical schemes to each type. All material included is presented free of specialized notation and terminology.

Wiley, 2011. - 512 pages. A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs,...

Department of Mathematics Naval Postgraduate School, 2003. - 248 pages. This course is designed to respond to the needs of the aeronautical engineering curricula by providing an applications oriented introduction to the finite difference method of solving partial differential equations arising from various physical phenomenon. This course will emphasize design, coding, and debugging programs written by the students in order to fix ideas presente...

Elsevier Science & Technology, 1983. - 688 Pages. Six invited papers on computational methods of solving partial differential equations were presented at the 1981 Conference on Numerical Solutions of Partial Differential Equations held at the University of Melbourne, Australia. They were also printed as part of the Conference Proceedings titled Numerical Solutions of Partial Differential Equations, edited by J. Noye and published by the Nort...

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...

Springer, 2009. - 619 Pages. In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underl...

Trangenstein J.A. Numerical solution of hyperbolic partial differential equations Department of Mathematics, Duke University Durham, NC 27708-0320 Cambridge University Press 2007. Hyperbolic conservation laws describe a number of interesting physical problems in diverse areas such as ?uid dynamics, solid mechanics, and astrophysics. Our emphasis in this book is on nonlinearities in these problems, especially those that lead to the development of...