Explicit fixed-step solver of third order. The method was proposed by Przemyslaw Bogacki and Lawrence F. Shampine in 1989. The Bogacki–Shampine method is a Runge–Kutta method of order three with four stages with the First Same As Last (FSAL) property, so that it uses approximately three function evaluations per step.

Low-order methods are more suitable than higher-order methods like the Dormand–Prince method of order five, if only a crude approximation to the solution is required. Bogacki and Shampine argue that their method outperforms other third-order methods with an embedded method of order two.

The Butcher tableau for the Bogacki–Shampine method is:

0 1/2 1/2 3/4 0 3/4 2/9 1/3 4/9 Applicable solver settings:

• Fixed-step size
• Limit data points to last

• http://en.wikipedia.org/wiki/Bogacki-Shampine