Continuous variable stepsize explicit pseudo two-step RK methods

✍ Scribed by Nguyen Huu Cong

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 598 KB
• Volume: 101
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(98)00199-x

✦ Synopsis

The aim of this paper is to apply a class of constant stepsize explicit pseudo two-step Runge-Kutta methods of arbitrarily high order to nonstiff problems for systems of first-order differential equations with variable stepsize strategy. Embedded formulas are provided for giving a cheap error estimate used in stepsize control. Continuous approximation formulas are also considered for use in an eventual implementation of the methods with dense output. By a few widely used test problems, we compare the efficiency of two pseudo two-step Runge-Kutta methods of orders 5 and 8 with the codes DOPRI5, DOP853 and PIRK8. This comparison shows that in terms off-evaluations on a parallel computer, these two pseudo two-step Runge-Kutta methods are a factor ranging from 3 to 8 cheaper than DOPRI5, DOP853 and PIRK8. Even in a sequential implementation mode, fifth-order new method beats DOPRI5 by a factor more than 1.5 with stringent error tolerances. (~) 1999 Elsevier Science B.V. All rights reserved.