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Table 1 Numerical results of solutions y(t) corresponding to Example 1

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

t Exact solution Approximate numerical solution
\(m=2\) \(m=3\) \(m=5\) \(m=7\) \(m=9\)
0.0 0.0000000000 0.0791342855 −  0.0867203112 0.0017122077 0.0000136462 −  0.0000009350
0.1 0.0430893512 0.1919158386 0.0630874540 0.0424955458 0.0430864782 0.0430890650
0.2 0.1440550329 0.2756498587 0.1858065079 0.1445339827 0.1440607936 0.1440552691
0.3 0.2625776389 0.3303363458 0.2814368505 0.2629329416 0.2625741070 0.2625775397
0.4 0.3658259586 0.3559752999 0.3499784820 0.3654360586 0.3658218164 0.3658258381
0.5 0.4316228960 0.3525667209 0.3914314023 0.4311192308 0.4316278591 0.4316231361
0.6 0.4489459081 0.3201106090 0.4057956114 0.4490846654 0.4489487670 0.4489457778
0.7 0.4165429404 0.2586069640 0.3930711092 0.4171549281 0.4165371068 0.4165428505
0.8 0.3404893353 0.1680557861 0.3532578958 0.3405669919 0.3404902893 0.3404895683
0.9 0.2314079965 0.0484570751 0.2863559712 0.2306662855 0.2314107365 0.2314077114
1.0 0.1018897407 −  0.1001891689 0.1923653355 0.1036007422 0.1019033887 0.1018888057