Knabner P., Angerman L. Numerical Methods for Elliptic and Parabolic Partial Differential Equations

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...

Academic Press, 1991. - 344 pages. Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places...

Springer, 2006. - 320 Pages. Meshfree methods for the numerical solution of partial differential equations are becoming more and more mainstream in many areas of applications. This volume represents the state-of-the-art in meshfree methods. It consists of articles which address the different meshfree techniques, their mathematical properties and their application in applied mathematics, physics and engineering.

Cambridge University Press, 1996. - 400 Pages This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutt...

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,...

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...

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...

Springer, 2008. - 544 Pages. This is the softcover reprint of the very popular hardcover edition. This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description...

Springer, 2010. - 500 pages. This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems in R^ 3. The book is self-contained, the prerequisites on elliptic partial differential and integral equations being presented in Chapters 2 and 3. The main focus is on the development, analysis, and implementation of...