solving ${f} = {{x}^{2}}$
euler
Gnuplot
Produced by GNUPLOT 5.4 patchlevel 4
-1x10
143
-9x10
142
-8x10
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-7x10
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-6x10
142
-5x10
142
-4x10
142
-3x10
142
-2x10
142
-1x10
142
0
1x10
142
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
x
correct x
correct x
Gnuplot
Produced by GNUPLOT 5.4 patchlevel 4
1x10
20
1x10
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1x10
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1x10
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1x10
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1x10
120
1x10
140
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
error
error
midpoint
Gnuplot
Produced by GNUPLOT 5.4 patchlevel 4
-1.2x10
143
-1x10
143
-8x10
142
-6x10
142
-4x10
142
-2x10
142
0
2x10
142
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
x
correct x
correct x
Gnuplot
Produced by GNUPLOT 5.4 patchlevel 4
1x10
20
1x10
40
1x10
60
1x10
80
1x10
100
1x10
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1x10
140
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
error
error
trapezoid
Gnuplot
Produced by GNUPLOT 5.4 patchlevel 4
-1.2x10
143
-1x10
143
-8x10
142
-6x10
142
-4x10
142
-2x10
142
0
2x10
142
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
x
correct x
correct x
Gnuplot
Produced by GNUPLOT 5.4 patchlevel 4
1x10
20
1x10
40
1x10
60
1x10
80
1x10
100
1x10
120
1x10
140
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
error
error
simpson
Gnuplot
Produced by GNUPLOT 5.4 patchlevel 4
-9x10
142
-8x10
142
-7x10
142
-6x10
142
-5x10
142
-4x10
142
-3x10
142
-2x10
142
-1x10
142
0
1x10
142
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
x
correct x
correct x
Gnuplot
Produced by GNUPLOT 5.4 patchlevel 4
1x10
20
1x10
40
1x10
60
1x10
80
1x10
100
1x10
120
1x10
140
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
error
error