RKF-ABM2010

RKF-ABM2010 - 10/18/2010 RUNGE-KUTTA-FEHLBERG &...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
10/18/2010 1 R UNGE -K UTTA -F EHLBERG & A DMAS -B ASHFORTH -M OULTON Xin Li (10/18/2010) | The step length h determines the precision. | One practical way to estimate accuracy in the One practical way to estimate accuracy in the numerical solution of an I.V.P. is to solve the problem twice using step sizes h and h/2 and compare answers at the mesh points corresponding to the larger step size. | (i) Using RK to obtain y(t n +h) with step length h ; and (ii) using RK to obtain y*(t n +h) . With step length h/2 . Check to see if |y-y*| < η (prescribed error tolarence). | But this requires a significant amount of computation for the smaller step size and must be repeated if it is determined that the agreement is not good enough.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
10/18/2010 2 A UTOMATICALLY A DJUSTING S TEP S IZE | The Runge-Kutta-Fehlberg method (denoted RKF45) is one way to try to resolve this problem. | It has a procedure to determine if the proper step size h is being used . | At each step, two different approximations for the solution are made and compared.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

RKF-ABM2010 - 10/18/2010 RUNGE-KUTTA-FEHLBERG &amp;...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online