2158f3eb-7e22-41eb-a257-9b61e93e3ad0 16 3 5 decimal

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Analysing Rkadapt

In this example, we give ourself a target value from other source for comparative purpose wrt Rkadapt stability. An adopted step size is generally taken not to exceed 0.001 the range of the solution. This demo reveals that much smaller step size will be as good. Maybe not a good rule, unless not exigent about accuracy and if the computation time is of concern. We could use the target value to discriminate the Δ's at once [just not done so !]

Rkadapt 50 1.494287 75 1.493620 100 1.493438 125 1.493402 150 1.496460 175 1.495543 200 1.495040 225 1.494573 250 1.494318 275 1.494047 300 1.493899 325 1.493733 350 1.493641 375 1.493533 400 1.493470 425 1.493421 450 1.493357 475 1.493323 500 1.493287 525 1.493246 202 mat :

x f x - exp x sqrt / :

ε 107 -^:

target 1.493648 :

N 125 :

max 'N' ... < 10000 ... unknown sol 0 ε 1 N x f Rkadapt :

sol N 1 + row 1.000000 1.493402 12 mat

Follow Rkadapt cumulative solving steps

sol 1 2 1 1 2 2 mat 1 target o 7 green 1 5 mat 3 1 sys

Function to be integrated

x f 1 2 1 2 - 2 2 mat 2 1 sys

ε f 3162

The puzzling dn_GearsBDF wrt last solution

n 1000 :

SOL 0 ε 1 n x f dn_GearsBDF :

SOL rows 1001

apparent cycling solutions SOL n 0 - row 0.999000 1.493088 12 mat

fixed value, no matter 'n' SOL n 1 + row 1.000000 1.493457 12 mat

Expose Rkadapt step size 'n'

Rkadapt Rkadapt 120 range 12 range el :

stability Rkadapt 1 col Rkadapt 2 col 1.49 - augment :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

Analysing Rkadapt stability

stability 3 BarSize