Error propagation

Errors in the initial data or errors in the first calculations (truncationarrors and/or round-off errors) wil affect the accuracy of the next calculated values in any method. We say that errors propagate through the calculation. Some methods will be very sensitive to small variations in the starting values used in a particular step. This means that small errors are quickly blown up. Such methods are unstable . Stable methods do not unduly magnify already existing errors. We might see more detailed discussions on the stability of certain numerical methods.