Application of Weighted Residual Methods to Dynamic Economic Models

Abstract

Abstract 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.

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