Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications

Table 1

Comparison of the actual and estimate absolute errors for 𝑁=2,3 and 𝑀=3,4,5 of Example 4.

𝑡𝑖	The actual absolute errors	Estimate absolute errors
	𝑒2(𝑡𝑖)=|𝑦(𝑡𝑖)−𝑦2(𝑡𝑖)|	|𝑒2,3(𝑡𝑖)|	|𝑒2,4(𝑡𝑖)|
0	4.0000𝑒−09	0	3.4000𝑒−10
0.2	2.1080𝑒−04	2.0730𝑒−04	2.1080𝑒−04
0.4	7.7779𝑒−04	7.8162𝑒−04	7.7778𝑒−04
0.6	1.0039𝑒−03	1.0076𝑒−03	1.0039𝑒−03
0.8	1.5349𝑒−04	1.5161𝑒−04	1.5346𝑒−04
1	3.1644𝑒−04	3.1748𝑒−04	3.1646𝑒−04
	|𝑒3(𝑡𝑖)|=|𝑦(𝑡𝑖)−𝑦3(𝑡𝑖)|	|𝑒3,4(𝑡𝑖)|	|𝑒3,5(𝑡𝑖)|
0	4.4000𝑒−09	7.0000𝑒−10	8.5000𝑒−10
0.2	3.5096𝑒−06	3.5003𝑒−06	3.5037𝑒−06
0.4	3.8180𝑒−06	3.8078𝑒−06	3.8252𝑒−06
0.6	3.7010𝑒−06	3.6681𝑒−06	3.6935𝑒−06
0.8	1.8690𝑒−06	1.8527𝑒−06	1.8792𝑒−06
1	1.0250𝑒−06	1.0301𝑒−06	1.0370𝑒−06