Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems

Table 4

The error histories at the selected points for Example 6.

𝑡	Bessel Int 𝑁=8	Bessel Int 𝑁=12	Bessel Int 𝑁=20	PM for 𝑁=8	PM for 𝑁=12	PM for 𝑁=20
0.0	9.6890𝑒−003	6.6498𝑒−003	4.1214𝑒−003	0	0	0
0.1	2.3974𝑒−002	1.0755𝑒−002	1.6289𝑒−003	6.5649𝑒−009	6.8945𝑒−014	6.1062𝑒−014
0.2	7.2706𝑒−003	1.6306𝑒−003	4.6111𝑒−003	4.5248𝑒−009	5.0071𝑒−014	4.8073𝑒−014
0.3	2.5780𝑒−003	4.6009𝑒−003	8.9332𝑒−003	3.6167𝑒−009	4.1522𝑒−014	3.7859𝑒−014
0.4	2.2427𝑒−003	7.2766𝑒−003	1.1642𝑒−002	3.2895𝑒−009	3.3973𝑒−014	3.0309𝑒−014
0.5	6.3782𝑒−003	1.0152𝑒−002	1.3160𝑒−002	2.2422𝑒−009	2.7311𝑒−014	2.4425𝑒−014
0.6	6.9801𝑒−003	1.1190𝑒−002	1.3796𝑒−002	2.4272𝑒−009	2.2649𝑒−014	1.9873𝑒−014
0.7	9.5374𝑒−003	1.1427𝑒−002	1.3807𝑒−002	1.1916𝑒−009	1.8097𝑒−014	1.6431𝑒−014
0.8	8.6910𝑒−003	1.1990𝑒−002	1.3398𝑒−002	1.8602𝑒−009	1.0991𝑒−014	1.3878𝑒−014
0.9	1.0169𝑒−002	1.1068𝑒−002	1.2680𝑒−002	4.0343𝑒−009	6.6391𝑒−014	1.8874𝑒−014
1.0	5.8131𝑒−003	8.4105𝑒−003	1.0482𝑒−002	2.2065𝑒−007	3.9901𝑒−012	8.3072𝑒−012