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

Table 2

The error histories at the selected points for Example 4.

𝑡	PM for 𝑁=4	PM for 𝑁=5	PM for 𝑁=6	TFM [30] 𝑁=6	MGL [31] 𝑁=6	TFM [30] 𝑁=64
0.0	1.5274𝑒−003	3.5407𝑒−005	6.8533𝑒−007	7.4890𝑒−002	9.3400𝑒−002	7.6980𝑒−003
0.1	1.9116𝑒−003	6.7725𝑒−005	1.4752𝑒−006	2.2140𝑒−002	1.0020𝑒−001	1.6770𝑒−003
0.2	2.3352𝑒−003	9.5549𝑒−005	1.7583𝑒−006	5.2150𝑒−002	1.0660𝑒−001	5.6050𝑒−003
0.3	2.6500𝑒−003	9.9318𝑒−005	1.8482𝑒−006	7.1120𝑒−002	1.5530𝑒−001	5.8040𝑒−003
0.4	2.8209𝑒−003	1.0115𝑒−004	2.2289𝑒−006	1.5220𝑒−002	2.3530𝑒−001	2.0900𝑒−003
0.5	2.9118𝑒−003	1.1223𝑒−004	2.5894𝑒−006	9.9270𝑒−002	2.9390𝑒−001	1.0200𝑒−002
0.6	2.9909𝑒−003	1.1855𝑒−004	2.3877𝑒−006	2.8060𝑒−002	2.7180𝑒−001	1.9860𝑒−003
0.7	3.0063𝑒−003	1.0774𝑒−004	2.1119𝑒−006	5.7040𝑒−002	1.7540𝑒−001	5.9630𝑒−003
0.8	2.7289𝑒−003	9.2586𝑒−005	2.4315𝑒−006	6.5130𝑒−002	7.5600𝑒−002	5.5260𝑒−003
0.9	1.8221𝑒−003	8.1824𝑒−005	1.6928𝑒−006	1.5240𝑒−002	1.8200𝑒−002	1.7450𝑒−003