Variational Iteration Method for Volterra Functional Integrodifferential Equations with Vanishing Linear Delays

Table 3

Comparison of the approximate solutions 𝑢_𝑖(𝑡)  𝑖=1,2,3,4 for 𝑞=0.5,0.9 obtained by VIM and exact solution for Example 3.

𝑡	Exact solution; exp(−𝑡)	𝑞=0.5
		𝑢1(𝑡)	𝑢2(𝑡)	𝑢3(𝑡)	𝑢4(𝑡)
0.0	1	1	1	1	1
0.1	0.9048374181	0.90497942450071400910	0.90483748741107270427	0.90483741805242138249	0.90483741803596200471
0.2	0.8187307531	0.81983741803595957315	0.81873293384360849615	0.81873075515690256459	0.81873075307914074618
0.3	0.7408182207	0.74445797642505780725	0.74083449149857746742	0.74081825573123809853	0.74081822072579434996
0.4	0.6703200461	0.67873075307798185865	0.67038742657940433398	0.67032030516271146820	0.67032004661645207518
0.5	0.6065306597	0.62255078307140486825	0.60673277637280939642	0.60653187925220335286	0.60653066399458711921
0.6	0.5488116361	0.57581822068171786605	0.54930607270835810138	0.54881594959954198138	0.54881165795778522201
0.7	0.4965853038	0.53843808971871343435	0.49763612853757107135	0.49659783161461355313	0.49658539043431628837
0.8	0.4493289641	0.51032004603563930075	0.45134388453293573575	0.44936046249936186908	0.44932924933896528241
0.9	0.4065696598	0.49137815162177329315	0.41014131275885829432	0.40664059717392117254	0.40657047465503823667
1.0	0.3678794412	0.48153065971263342360	0.37383037461088097827	0.36802591071733624760	0.36788152336102633522
𝑡	Exact solution	𝑞=0.9
		𝑢1(𝑡)	𝑢2(𝑡)	𝑢3(𝑡)	𝑢4(𝑡)
0.0	1	1	1	1	1
0.1	0.9048374181	0.90493399181734899264	0.90483745074109448289	0.90483741804170096412	0.90483741803596020044
0.2	0.8187307531	0.81948345078404001183	0.81873178064764946164	0.81873075380246128715	0.81873075307829932576
0.3	0.7408182207	0.74329416352047399205	0.74082588393681840739	0.74081823288648341576	0.74081822069378094348
0.4	0.6703200461	0.67604240337279503178	0.67035176736152140112	0.67032013619892943843	0.67032004619445398093
0.5	0.6065306597	0.61743230645654071842	0.60662577333757734681	0.60653108373872136469	0.60653066088242863204
0.6	0.5488116361	0.56719347354110536945	0.54904422318813049430	0.54881313480065468329	0.54881164206183218979
0.7	0.4965853038	0.52507877833716510528	0.49707944364786691003	0.49658965350944597168	0.49658532742084464384
0.8	0.4493289641	0.49086236442220647225	0.45027614299614648238	0.44933989316560210393	0.44932904183882139059
0.9	0.4065696598	0.46433781456830063028	0.40824810613286514749	0.40659425703516855802	0.40656988162052589374
1.0	0.3678794412	0.44531647763366617328	0.37067518059820559824	0.36793019699837690354	0.36788000764693672188