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Numerical solution of ordinary differential equations

In ordinary differential equations the unknown function depends only on one variable. Therefore only ordinary derivatives of the function in this one variable 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 variable. Thus, the differential equation describing the changing behavior of the required quantities.

Only for a few differential equations exist explicit algorithms to solve. For many solutions is not even an explicit solution representation possible so that here much resorting to numerical approximation.