Approximation Algorithm for a System of Pantograph Equations

Table 3

Comparison of the absolute errors for Example 3.3.

t	Exact solution	𝑢1
	𝑢1=−cos(𝑡)	𝑛=1	𝑛=2	𝑛=3
0.2	9.800658𝐸−1	2.124𝐸−2	1.525𝐸−4	8.904𝐸−5
0.4	9.210610𝐸−1	8.908𝐸−2	2.474𝐸−3	1.511𝐸−3
0.6	8.253356𝐸−1	2.074𝐸−1	3.267𝐸−2	8.051𝐸−3
0.8	6.967067𝐸−1	3.764𝐸−1	4.042𝐸−2	2.665𝐸−2
1.0	5.403023𝐸−1	5.920𝐸−1	1.934𝐸−1	6.766𝐸−2
	𝑢2=𝑡cos(𝑡)	𝑢2
		𝑛=1	𝑛=2	𝑛=3
0.2	1.960133𝐸−1	1.329𝐸−3	1.935𝐸−4	5.496𝐸−6
0.4	3.684244𝐸−1	1.052𝐸−2	5.824𝐸−3	1.808𝐸−4
0.6	4.952014𝐸−1	3.489𝐸−2	1.139𝐸−2	1.408𝐸−3
0.8	5.573654𝐸−1	8.071𝐸−2	2.312𝐸−2	6.069𝐸−3
1.0	5.403023𝐸−1	1.528𝐸−1	1.078𝐸−1	1.890𝐸−2
	𝑢3=sin(𝑡)	𝑢3
		𝑛=1	𝑛=2	𝑛=3
0.2	1.986693𝐸−1	2.7285𝐸−3	1.4629𝐸−3	6.4558𝐸−5
0.4	3.894183𝐸−1	2.2245𝐸−2	1.2666𝐸−2	9.9595𝐸−4
0.6	5.646425𝐸−1	7.6209𝐸−2	4.5691𝐸−2	4.8397𝐸−3
0.8	7.173561𝐸−1	1.8264𝐸−1	1.1440𝐸−1	1.4613𝐸−2
1.0	8.414710𝐸−1	3.5930𝐸−1	2.3340𝐸−1	3.3917𝐸−2