An efficient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration

Journal of the Egyptian Mathematical Society

Table 3 Numerical results of solutions y(t) corresponding to Example 2

t	Exact solution	Approximate numerical solution
t	Exact solution	\(m=2\)	\(m=3\)	\(m=5\)	\(m=7\)	\(m=9\)
0.0	0.0000000000	− 0.0073937153	− 0.0040027165	0.0001187872	0.0000022238	− 0.0000000886
0.1	0.0043242326	0.0060536044	0.0055340385	0.0042852305	0.0043240016	0.0043242054
0.2	0.0146277221	0.0181146026	0.0162203655	0.0146643552	0.0146284149	0.0146277447
0.3	0.0272688450	0.0287892791	0.0273042888	0.0272894001	0.0272682392	0.0272688349
0.4	0.0394275753	0.0380776340	0.0380338327	0.0393956406	0.0394272213	0.0394275646
0.5	0.0492917976	0.0459796673	0.0476570217	0.0492590084	0.0492925214	0.0492918201
0.6	0.0560187959	0.0524953789	0.0554218801	0.0560347104	0.0560189543	0.0560187830
0.7	0.0595522819	0.0576247689	0.0605764323	0.0595958489	0.0595515045	0.0595522742
0.8	0.0603722504	0.0613678373	0.0623687027	0.0603720403	0.0603725898	0.0603722720
0.9	0.0592403619	0.0637245841	0.0600467155	0.0591880351	0.0592405489	0.0592403351
1.0	0.0569836042	0.0646950092	0.0528584952	0.0571023372	0.0569858282	0.0569835156