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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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Application of Weighted Residual Methods to Dynamic Economic Models

Application of Weighted Residual Methods to Dynamic Economic Models

Chapter:
(p.114) 6 Application of Weighted Residual Methods to Dynamic Economic Models
Source:
Computational Methods for the Study of Dynamic Economies
Author(s):

Ellen R. McGrattan

Publisher:
Oxford University Press
DOI:10.1093/0199248273.003.0006

Many problems in economics require the solution to a functional equation as an intermediate step, and typically, decision functions are sought that satisfy a set of Euler conditions or a value function that satisfies Bellman's equation. However, in many cases, analytical solutions cannot be derived for these functions, and numerical methods are needed instead. Shows how to apply weighted residual and finite‐element methods to this type of problem by illustrating their application to various examples. The first type of problem involves a simple differential equation because the coefficients to be computed satisfy a linear system of equations, and no computer is needed for the solution. Weighted residual and finite‐element methods are then applied to a deterministic growth model and a stochastic growth model—two standard models used in economics; in these examples, the coefficients to be computed satisfy nonlinear systems of equations, which, fortunately, are exploitably sparse if they are derived from a finite‐element method.

Keywords:   deterministic growth models, differential equations, dynamic economics models, finite‐element methods, functional equations, growth models, linear models, macroeconomics, nonlinear models, solution methods, stochastic growth models, weighted residual methods

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