Stiffness of ODEs

General purpose methods adapt the step size to the solution of the problem, and they also adapt the order of the method, which allows both high accuracy and stability. The stability of the methods generally becomes worse as the order increases. The maximum order can be specified for stability reasons. A simple numerical experiment can be used to show how the selection of ODE solver affects a solution. Consider Example 6.6, which becomes stiff for large a values. 

We can draw several conclusions from Table 6.4 after what we have learned in this chapter. We can conlude that for non-stiff problems and moderate error tolerances all methods work efficiently. When the error tolerance is stricter, the higher-order method ode45 performs better than the ode23 method. 

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