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

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