Solving differential equations

In the example in the previous section, the solution of the differential equation

$\displaystyle \dot{x}=f(x)$ (5.4)

could be computed analytically. Although this is always possible for linear differential equations, in general no analytical solution exists. In that case, one has to use numerical solution techniques to approximate a solution.

Usually, solving a differential equation numerically requires a correct solver to obtain accurate results. However, a numerical obtained solution will give an engineer less information as an analytical expression. For example, with a complete algebraic expression, it may be possible to determine the trajectory for different initial conditions or prove stability of a system. In general, a new numerical solution has to be found, when e.g. the initial conditions change.

The following section explains the use of numerical solvers, and how to interpret the results. In Section 5.3, the use of MATLAB for analytical solutions of differential equations is discussed.

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Esteur 2010-03-22