Runge-Kutta applied to a scalar initial value problem
dy/dt(t)=2*y/t + t^2*exp(t), y(1)=0

Approxs. for grid of 10 every 1 grid points

 t(1)= 1.10000000e+000 y(1)= 3.45910287e-001
t(2)= 1.20000000e+000 y(2)= 8.66621693e-001
t(3)= 1.30000000e+000 y(3)= 1.60718135e+000
t(4)= 1.40000000e+000 y(4)= 2.62031131e+000
t(5)= 1.50000000e+000 y(5)= 3.96760190e+000
t(6)= 1.60000000e+000 y(6)= 5.72087932e+000
t(7)= 1.70000000e+000 y(7)= 7.96377179e+000
t(8)= 1.80000000e+000 y(8)= 1.07935018e+001
t(9)= 1.90000000e+000 y(9)= 1.43229357e+001
t(10)= 2.00000000e+000 y(10)= 1.86829266e+001

Approxs. for grid of 100 every 10 grid points

 t(10)= 1.10000000e+000 y(10)= 3.45919875e-001
t(20)= 1.20000000e+000 y(20)= 8.66642533e-001
t(30)= 1.30000000e+000 y(30)= 1.60721507e+000
t(40)= 1.40000000e+000 y(40)= 2.62035955e+000
t(50)= 1.50000000e+000 y(50)= 3.96766629e+000
t(60)= 1.60000000e+000 y(60)= 5.72096152e+000
t(70)= 1.70000000e+000 y(70)= 7.96387347e+000
t(80)= 1.80000000e+000 y(80)= 1.07936246e+001
t(90)= 1.90000000e+000 y(90)= 1.43230815e+001
t(100)= 2.00000000e+000 y(100)= 1.86830971e+001

Approxs. for grid of 1000 every 100 grid points

 t(100)= 1.10000000e+000 y(100)= 3.45919877e-001
t(200)= 1.20000000e+000 y(200)= 8.66642536e-001
t(300)= 1.30000000e+000 y(300)= 1.60721508e+000
t(400)= 1.40000000e+000 y(400)= 2.62035955e+000
t(500)= 1.50000000e+000 y(500)= 3.96766629e+000
t(600)= 1.60000000e+000 y(600)= 5.72096153e+000
t(700)= 1.70000000e+000 y(700)= 7.96387348e+000
t(800)= 1.80000000e+000 y(800)= 1.07936247e+001
t(900)= 1.90000000e+000 y(900)= 1.43230815e+001
t(1000)= 2.00000000e+000 y(1000)= 1.86830971e+001
 
       h          Error(Max)
  1.0000e-001    1.7051e-004
  1.0000e-002    2.0347e-008
  1.0000e-003    1.0409e-012
 
Least squares fit gives E(h) = 2.51322 * h^4.10717
 
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