A new fourth order Runge-Kutta formula for y′ = Ay with stepsize control

✍ Scribed by B.B. Sanugi; D.J. Evans

• Book ID: 108020281
• Publisher: Elsevier Science
• Year: 1988
• Tongue: English
• Weight: 245 KB
• Volume: 15
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(88)90134-4

✦ Synopsis

Abmraet--A new fourth order Runge-Kutta method for solving linear initial value problems of the form y'= Ay is derived which provides an estimate of the truncation error without any extra function evaluations. The idea follows from the fact that two numerical solutions of similar order can be obtained by using the arithmetic mean (AM) and the geometric mean (GM) averaging of the functional values. The numerical results given confirm that this new method is suitable to be used as an error control strategy.