The initial value problem being solved is y' = -y + 2 cos x, y(0)=1 The true solution is Y = sin x + cos x RESULTS USING THE "MIDPOINT" RUNGE-KUTTA METHOD OF ORDER 2 EQUATION 3 XZERO= 0.00E+00 B= 2.00E+01 YZERO= 1.00000E+00 STEPSIZE= 2.000E-01 PRINT PARAMETER= 10 X= 2.000E+00 Y(X)= 4.8688872118E-01 ERROR= 6.26E-03 X= 4.000E+00 Y(X)=-1.4077907467E+00 ERROR=-2.66E-03 X= 6.000E+00 Y(X)= 6.8445524579E-01 ERROR=-3.70E-03 X= 8.000E+00 Y(X)= 8.3807468173E-01 ERROR= 5.78E-03 X= 1.000E+01 Y(X)=-1.3819861389E+00 ERROR=-1.11E-03 X= 1.200E+01 Y(X)= 3.1214272564E-01 ERROR=-4.86E-03 X= 1.400E+01 Y(X)= 1.1221915979E+00 ERROR= 5.15E-03 X= 1.600E+01 Y(X)=-1.2461357098E+00 ERROR= 5.73E-04 X= 1.800E+01 Y(X)=-8.5040733172E-02 ERROR=-5.63E-03 X= 2.000E+01 Y(X)= 1.3169145736E+00 ERROR= 4.11E-03 EQUATION 3 XZERO= 0.00E+00 B= 2.00E+01 YZERO= 1.00000E+00 STEPSIZE= 1.000E-01 PRINT PARAMETER= 20 X= 2.000E+00 Y(X)= 4.9168884124E-01 ERROR= 1.46E-03 X= 4.000E+00 Y(X)=-1.4097776421E+00 ERROR=-6.68E-04 X= 6.000E+00 Y(X)= 6.8158572231E-01 ERROR=-8.31E-04 X= 8.000E+00 Y(X)= 8.4248804595E-01 ERROR= 1.37E-03 X= 1.000E+01 Y(X)=-1.3827845660E+00 ERROR=-3.08E-04 X= 1.200E+01 Y(X)= 3.0839461306E-01 ERROR=-1.11E-03 X= 1.400E+01 Y(X)= 1.1261096554E+00 ERROR= 1.23E-03 X= 1.600E+01 Y(X)=-1.2456485579E+00 ERROR= 8.58E-05 X= 1.800E+01 Y(X)=-8.9364242231E-02 ERROR=-1.31E-03 RESULTS USING THE "TRAPEZOIDAL" RUNGE-KUTTA METHOD OF ORDER 2 EQUATION 3 XZERO= 0.00E+00 B= 2.00E+01 YZERO= 1.00000E+00 STEPSIZE= 2.000E-01 PRINT PARAMETER= 10 X= 2.000E+00 Y(X)= 4.8486041171E-01 ERROR= 8.29E-03 X= 4.000E+00 Y(X)=-1.3998711854E+00 ERROR=-1.06E-02 X= 6.000E+00 Y(X)= 6.8074864988E-01 ERROR= 6.14E-06 X= 8.000E+00 Y(X)= 8.3335782041E-01 ERROR= 1.05E-02 X= 1.000E+01 Y(X)=-1.3743375483E+00 ERROR=-8.76E-03 X= 1.200E+01 Y(X)= 3.1049593741E-01 ERROR=-3.21E-03 X= 1.400E+01 Y(X)= 1.1159139244E+00 ERROR= 1.14E-02 X= 1.600E+01 Y(X)=-1.2392640116E+00 ERROR=-6.30E-03 X= 1.800E+01 Y(X)=-8.4482324819E-02 ERROR=-6.19E-03 X= 2.000E+01 Y(X)= 1.3095781165E+00 ERROR= 1.14E-02 EQUATION 3 XZERO= 0.00E+00 B= 2.00E+01 YZERO= 1.00000E+00 STEPSIZE= 1.000E-01 PRINT PARAMETER= 20 X= 2.000E+00 Y(X)= 4.9121567262E-01 ERROR= 1.93E-03 X= 4.000E+00 Y(X)=-1.4078986288E+00 ERROR=-2.55E-03 X= 6.000E+00 Y(X)= 6.8069672329E-01 ERROR= 5.81E-05 X= 8.000E+00 Y(X)= 8.4137633946E-01 ERROR= 2.48E-03 X= 1.000E+01 Y(X)=-1.3809665794E+00 ERROR=-2.13E-03 X= 1.200E+01 Y(X)= 3.0799372622E-01 ERROR=-7.13E-04 X= 1.400E+01 Y(X)= 1.1246253930E+00 ERROR= 2.72E-03 X= 1.600E+01 Y(X)=-1.2440123195E+00 ERROR=-1.55E-03 X= 1.800E+01 Y(X)=-8.9241809407E-02 ERROR=-1.43E-03