Differential equations
Differential equations are equations whose solutions are not numbers but functions. They describe the relationship that should exist between the searched function and its derivatives.
A distinction is made between ordinary and partial differential equations.
- On ordinary differential equations the unknown function depends only on one variable. Therefore only ordinary derivatives of the function can occur. The order of the differential equation is the highest occurring derivative. One differentiates between explicit and implicit differential equations, depending on whether you can solve the equation for the highest occurring derivative or not. In application often the time is the variables. Thus, the differential equation describing the changing behavior of the required quantities.
- On partial differential equations the unknown function depends on more than one variable and also contain derivatives with respect to more than one of these variables. There is a wide field of possible equations whose theory is the subject of current research in various fields.
Only for a few differential equations there are explicit algorithms to solve. For many solutions not even an explicit solution of the representation is possible so that often numerical approximation are used here.
