ABSTRACT
The use of high precision arithmetic with small step-sizes led to accurate solutions for the simple problems attempted. For many practical problems, the constant steplength approach is not recommended because the derivatives can vary significantly in magnitude. If the step-size were kept constant, the Runge–Kutta, or other process, is likely to deliver local errors which vary greatly from step to step according to the variability of the error functions. More sophisticated schemes, based on error estimates at two or more successive steps, have been devised for step–size control. These are employed in some computer packages for the solution of differential equations, but the simple method is very robust and reasonably efficient, particularly if the step amplification factor is restricted. The type of step-size control practised leads to numerical solutions being obtained for values of the independent variable not predictable for more than a single step ahead.
