Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
On Stability of LMS Methods and Characteristic Roots of Delay Differential Equations
SIAM Journal on Numerical Analysis
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Dynamic economic models generally consist in difference or differential behavioral equations. Several arguments are in favor of continuous time systems: the multiplicity of decisions overlapping in time, a more adequate formulation of market adjustments and distributed lag processes, the properties of estimators, etc. The type of dynamic equations also refers to historical and practical reasons. In some cases of the economic dynamics, delay differential equations (DDEs) may be more suitable to a wide range of economic models. The dynamics of the Kalecki's business cycle model is represented by a linear first-order DDE with constant coefficients, in the capital stock. Such a DDE, with constant or flexible lags, also occurs in the continuous time Solow's vintage capital growth model. This is due to the heterogeneity of goods and assets. In some qualitative study, the time delay is replaced by the Taylor series for a sufficiently small delay and a not too large higher-order derivative. DDEs with constant lags may be preferably solved by using Laplace transforms. Numerous techniques are also proposed for the solution of DDEs, like the inverse scattering method, the Jacobian elliptic function method, numerical techniques, the differential transform method, etc. This study uses a block diagram approach with application to reference economic models, with help of the software MATHEMATICA 6.0. and its specialized packages for signal processing, such as "Control System Professional".