A second-order integrator computes the ratio of a perturbed orbit's period to its…

PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Research software practice, verification and validation · Research software practice, verification and validation

Scientific Computing for Physicists, Ch Are they the right equations? Solution verification, benchmarks and validation

Problem

A second-order integrator computes the ratio

T/T_0

of a perturbed orbit's period to its unperturbed value on three grids of time steps per orbit, refinement ratio

r=2

N=40

gives

f_3=1.491000

N=80

gives

f_2=1.497400

N=160

gives

f_1=1.500000

(subscript 1 is the finest grid,

f

dimensionless). The integrator has already passed an order-of-accuracy test on a problem with a known answer. ((a)) Compute the observed order

\hat p

. ((b)) Is this study in the asymptotic range? May

\mathrm{GCI}_{\rm fine}

with

F_s = 1.25

be reported for

f_1

? If not, what should be done next?

Browse the problem library