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Computational Methods for the Study of Dynamic Economies$
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Ramon Marimon and Andrew Scott

Print publication date: 2001

Print ISBN-13: 9780199248278

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0199248273.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 11 November 2019

Finite‐Difference Methods for Continuous‐Time Dynamic Programming

Finite‐Difference Methods for Continuous‐Time Dynamic Programming

Chapter:
(p.172) 8 Finite‐Difference Methods for Continuous‐Time Dynamic Programming
Source:
Computational Methods for the Study of Dynamic Economies
Author(s):

Graham V. Candler

Publisher:
Oxford University Press
DOI:10.1093/0199248273.003.0008

Introduces some of the methods and underlying ideas behind computational fluid dynamics—in particular, the use is discussed of finite‐difference methods for the simulation of dynamic economies. A standard stochastic dynamic programming model is considered of a macroeconomy. Finite‐difference methods are applied to this problem (model), resulting in a second‐order nonlinear partial differential equation that has some features in common with the governing equations of fluid dynamics; the idea is also introduced of ‘upwind’ or solution‐dependent differencing methods, and the stability of these is discussed through the analysis of model problems. An implicit solution to the nonlinear dynamic programming problem is then developed and tested, with the motivation of reducing the computer time required to solve it. Finally, the extension of the finite‐difference method to a two‐state dynamic programming problem is considered.

Keywords:   computational fluid dynamics, dynamic economics models, dynamic economies, finite‐difference methods, macroeconomics, nonlinear dynamic programming models, nonlinear partial differential equations, solution‐dependent differencing methods, stochastic dynamic programming models, two‐state dynamic programming models

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