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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.
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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.
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This note was uploaded on 11/27/2011 for the course MATH 3484 taught by Professor Staff during the Fall '10 term at University of Central Florida.

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