Global and Local Errors in Runge-Kutta Methods

This Demonstration shows the global and local errors generated by a one-step Runge–Kutta method in the numerical solution of initial value problems. The local errors are from the exact solution. For several initial value problems, you can select the number of steps, the initial value , the end point of the interval of integration , and an explicit Runge–Kutta method with order less than or equal to 2. You can also plot the local and/or global errors.

THINGS TO TRY

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DETAILS

For problems 2 and 6, some stability problems can appear when you vary the number of steps and the integration interval.
Problem 8 is a discontinuous initial value problem; is the unit-step function, for and for . Therefore all the considered integration methods present some difficulties.
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