Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Numerical modelling in biosciences using delay differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
On Stability of LMS Methods and Characteristic Roots of Delay Differential Equations
SIAM Journal on Numerical Analysis
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In some cases of the economic macrodynamics, 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. 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 retains the Zhou's differential transform method for solving nonlinear DDEs with backward-foreward delays and flexible coefficients. This study also uses a block diagram approach with application to reference economic models, with help of the software MATHEMATICA 7.0.1 and its specialized packages for signal processing, such as "Control System Professional" and "SchematicSolver".