Enhanced moving least square method for the solution of volterra integro-differential equation: an interpolating polynomial

Taiwo, O. A.; Etuk, M. O.; Nwaeze, E.; Ogunniran, M. O.

doi:10.1186/s42787-022-00135-0

Journal of the Egyptian Mathematical Society

Table 5 Exact and MLS solutions at the given knots, CPU time = 0.75 s

From: Enhanced moving least square method for the solution of volterra integro-differential equation: an interpolating polynomial

x	Approximate u(x)	MLS u(x)	Exact U(x)	MLS error	MLS error (enhanced)
0	0	− 0.024655876676212	0	0.024655876676212	0
0.066666666666667	− 0.002379011893175	0.005537335586241	0.000001316872428	0.005536018713813	0.002380328765603
0.133333333333333	− 0.002200458335326	0.018361645942874	0.000042139917695	0.018319506025179	0.002242598253021
0.200000000000000	− 0.000209882115481	0.018910879661242	0.000320000000000	0.018590879661242	0.000529882115481
0.266666666666667	0.002519511299597	0.012394755114245	0.001348477366255	0.011046277747990	0.001171033933342
0.333333333333333	0.006117640493621	0.004251713602220	0.004115226337449	0.000136487264772	0.002002414156172
0.400000000000000	0.012015681631285	0.000071034716942	0.010240000000000	0.010168965283058	0.001775681631285
0.466666666666667	0.022823533748840	0.005268158970878	0.022132674897119	0.016864515926241	0.000690858851720
0.533333333333333	0.042460416868444	0.025004246618252	0.043151275720165	0.018147029101912	0.000690858851721
0.600000000000000	0.075984318368715	0.064305266155533	0.077760000000000	0.013454733844467	0.001775681631285
0.666666666666667	0.129684828642182	0.128063484798105	0.131687242798354	0.003623758000249	0.002002414156172
0.733333333333333	0.210912587465834	0.220886348193854	0.212083621399177	0.008802726794677	0.001171033933343
0.800000000000000	0.328209882115482	0.347116596621601	0.327680000000000	0.019436596621601	0.000529882115482
0.866666666666667	0.491188112656315	0.511170638717689	0.488945514403292	0.022225124314396	0.002242598253023
0.933333333333333	0.710625925473422	0.717685416786041	0.708245596707819	0.009439820078222	0.002380328765603
1.000000000000000	0.998551256887877	0.971372369628953	1.000000000000000	0.028627630371047	0.001448743112123

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