Topic
Numerical analysis
About: Numerical analysis is a research topic. Over the lifetime, 52236 publications have been published within this topic receiving 1224230 citations. The topic is also known as: numerical computation & numerical mathematics.
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TL;DR: In this paper, a numerical method for computing three-dimensional, time-dependent incompressible flows is presented based on a fractional-step, or time-splitting, scheme in conjunction with the approximate-factorization technique.
2,997 citations
Book•
01 Jan 1998
TL;DR: In this article, the authors present techniques from the numerical analysis and applied mathematics literatures and show how to use them in economic analyses, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods.
Abstract: To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A web site contains supplementary material including programs and answers to exercises.
2,880 citations
Book•
27 Aug 1999
TL;DR: In this article, the generalized Riemann problem is used to solve the Euler Equation problem and the ADER approach is used for non-linear systems with finite forces in multiple dimensions.
Abstract: The Equations of Fluid Dynamics.- Notions on Hyperbolic Partial Differential Equations.- Some Properties of the Euler Equations.- The Riemann Problem for the Euler Equations.- Notions on Numerical Methods.- The Method of Godunov for Non#x2014 linear Systems.- Random Choice and Related Methods.- Flux Vector Splitting Methods.- Approximate#x2014 State Riemann Solvers.- The HLL and HLLC Riemann Solvers.- The Riemann Solver of Roe.- The Riemann Solver of Osher.- High#x2013 Order and TVD Methods for Scalar Equations.- High#x2013 Order and TVD Schemes for Non#x2013 Linear Systems.- Splitting Schemes for PDEs with Source Terms.- Methods for Multi#x2013 Dimensional PDEs.- Multidimensional Test Problems.- FORCE Fluxes in Multiple Space Dimensions.- The Generalized Riemann Problem.- The ADER Approach.- Concluding Remarks.
2,811 citations
TL;DR: In this article, a numerical method for solving incompressible viscous flow problems is introduced, which uses the velocities and the pressure as variables and is equally applicable to problems in two and three space dimensions.
2,797 citations
Book•
01 Jan 1978
TL;DR: In this article, the authors present a solution to the Matrix Eigenvalue Problem for linear systems of linear equations, based on linear algebra and linear algebra with nonlinear functions, which they call linear algebraic integration.
Abstract: Error: Its Sources, Propagation, and Analysis. Rootfinding for Nonlinear Equations. Interpolation Theory. Approximation of Functions. Numerical Integration. Numerical Methods for Ordinary Differential Equations. Linear Algebra. Numerical Solution of Systems of Linear Equations. The Matrix Eigenvalue Problem. Appendix. Answers to Selected Problems. Index.
2,608 citations