On the Application of Genetic Algorithms to Differential Equations − Romanian Journal of Economic Forecasting – 2/2006 5 ON THE APPLICATION OF GENETIC ALGORITHMS TO DIFFERENTIAL EQUATIONS George Daniel MATEESCU * Abstract Genetic algorithms can be used in order to solve optimization problems. Such a technique may be used in order to solve differential equations. Key words: differential equations; genetic algorithms; JEL Classification: C61, C63 The main issue There are some fundamental econometric issues which lead to differential equations. For example, taking into account the demand-supply equilibrium, we may consider the variation of the price as being a ratio of the difference between demand and supply. ( ) () () P aDt St t ∆ = − ∆ where a is a positive constant. Assuming small values for t, we obtain the differential model: ( ) '( ) () () P t aDt St = − When demand exceeds supply, the right part represents a positive value, which implies that P is an increasing function. Formally, we may consider the general Cauchy problem 0 0 ' (, ), ( ) y fxy yx y = = , where x is the independent variable and () y yx = is the dependent variable. By using the classical assumption: [ ] [ ] 0 0 0 0 : , , f x Xx X y Yy Y − + × − + → R is continuous and satisfies the Lipschitz condition 1 2 1 2 (, ) (, ) f xy fxy Ly y − ≤ − * Romanian Academy, Institute for Economic Forecasting, e-mail: daniel@mateescu.ro. 1