The Runge-Kutta method

Step size

4th order

6th order

7th order

Error

Time in Second

Error

Time in Second

error

Time in Second

dt/1 = 0.01

Inf

1.4

Inf

6.2

Inf

3.9

Dt/2 = 0.005

2216.9968

1.4

Inf

6.0

Inf

4.2

Dt/4 = 0.0025

174.5643

1.4

320,083.898274

6.0

319,518.685882

3.8

Dt/8 = 0.00125

12.2611

1.4

2,539,526.94512

6.0

2,539,945.04633

3.8

dt/16 = 0.000625

0.8125

1.4

1,186,189.72471

6.0

1,189,148.66528

3.9

Dt/32 = 0.0003125

0.0523

1.4

273,214.706571

6.0

272,023.301318

3.7

Dt/64 = 0.00015625

0.0033

2.1

217,761.337783

6.0

216,946.587361

3.9

Dt/128 = 7.8125e−5

4.6614e−5

1.4

3204.148445892

6.0

3139.59110565

3.9

Dt/256 = 3.90625e−5

ERROR LIMIT SATISFIED

55.9530969299

6.0

55.7923759269

3.8

Dt/512 = 1.953125e5

2.735944731744

6.0

2.72836970305

3.8

Dt/1024 = 9.765625e−6

ERROR LIMIT SATISFIED

ERROR LIMIT SATISFIED

Total Time to execution

12.0

66.2

42.5