The ODE initial value problem being solved is
    y' = y cos(x),   y(0) = 1
The true solution is
    Y(x) = exp(sin x)

 Stepsize h=0.1

    x          Y(x)           Error          Error          Error
                             Order 2        Order 3        Order 4
  .000     1.00000000       .000E+00       .000E+00       .000E+00
 2.000     2.48257773      -.595E-02       .248E-04       .482E-05
 4.000      .46916419      -.431E-03      -.602E-04       .187E-05
 6.000      .75622563      -.739E-04      -.878E-05       .166E-05
 8.000     2.68950792      -.746E-02      -.163E-03       .110E-04
10.000      .58040966      -.142E-03      -.998E-04       .209E-05
12.000      .58474880      -.253E-03      -.244E-04       .230E-05
14.000     2.69286951      -.709E-02      -.379E-03       .117E-04
16.000      .74983409       .244E-03      -.148E-03       .182E-05
18.000      .47190044      -.398E-03      -.407E-04       .237E-05
20.000     2.49165027      -.503E-02      -.513E-03       .733E-05
  
 Stepsize h=0.05

    x          Y(x)           Error          Error          Error
                             Order 2        Order 3        Order 4
  .000     1.00000000       .000E+00       .000E+00       .000E+00
 2.000     2.48257773      -.151E-02       .276E-05       .304E-06
 4.000      .46916419      -.124E-03      -.730E-05       .119E-06
 6.000      .75622563      -.268E-04      -.854E-06       .967E-07
 8.000     2.68950792      -.193E-02      -.200E-04       .660E-06
10.000      .58040966      -.653E-04      -.122E-04       .127E-06
12.000      .58474880      -.783E-04      -.273E-05       .133E-06
14.000     2.69286951      -.189E-02      -.467E-04       .685E-06
16.000      .74983409       .119E-04      -.182E-04       .103E-06
18.000      .47190044      -.119E-03      -.477E-05       .134E-06
20.000     2.49165027      -.141E-02      -.638E-04       .389E-06
  
 Stepsize h=0.025

    x          Y(x)           Error          Error          Error
                             Order 2        Order 3        Order 4
  .000     1.00000000       .000E+00       .000E+00       .000E+00
 2.000     2.48257773      -.382E-03       .324E-06       .191E-07
 4.000      .46916419      -.329E-04      -.899E-06       .747E-08
 6.000      .75622563      -.768E-05      -.930E-07       .583E-08
 8.000     2.68950792      -.492E-03      -.249E-05       .405E-07
10.000      .58040966      -.200E-04      -.150E-05       .780E-08
12.000      .58474880      -.214E-04      -.323E-06       .799E-08
14.000     2.69286951      -.488E-03      -.581E-05       .415E-07
16.000      .74983409      -.308E-05      -.226E-05       .607E-08
18.000      .47190044      -.323E-04      -.580E-06       .797E-08
20.000     2.49165027      -.371E-03      -.797E-05       .222E-07