Modelling in economics using differential equations with delay

Modelling in economics using differential equations with delay

Paper in proceedings outside WoS and Scopus

Modern economic models are often constructed using functional differential equations (FDEs). With these equations, it is possible to construct models that are able to bring the described situations even closer to reality. These equations work with some sort of deformation of its arguments. Specifically, in our case, we introduce the so-called delay in these equations, which gives a subset of FDEs, namely, delay differential equations. These equations cannot be solved using classical known methods for solving ordinary differential equations (ODEs), and the theory around them is very little described in comparison with that of ODEs. In modern mathematical theory, we cannot do without the use of mathematical software, which are able, among other things, to solve this type of equations in certain cases, using basic methods for the solution. The described equations have found use in many economic applications, it is worth mentioning, for example, the model describing the so-called "shipbuilding cycle".

Modern economic models are often constructed using functional differential equations (FDEs). With these equations, it is possible to construct models that are able to bring the described situations even closer to reality. These equations work with some sort of deformation of its arguments. Specifically, in our case, we introduce the so-called delay in these equations, which gives a subset of FDEs, namely, delay differential equations. These equations cannot be solved using classical known methods for solving ordinary differential equations (ODEs), and the theory around them is very little described in comparison with that of ODEs. In modern mathematical theory, we cannot do without the use of mathematical software, which are able, among other things, to solve this type of equations in certain cases, using basic methods for the solution. The described equations have found use in many economic applications, it is worth mentioning, for example, the model describing the so-called "shipbuilding cycle".

dynamic models, delay differential equations, method of steps, method of characteristics, Shibuilding cycle

dynamic models, delay differential equations, method of steps, method of characteristics, Shibuilding cycle

MYŠKA, M.

2021

11.12.2020

Brno

Workshop specifického výzkumu 2020

152

161

332

https://www.konference.fbm.vutbr.cz/workshop/useruploads/files/sbornik/sbornik_workshop_2020.pdf