Research Article
Variational Iteration Method for Volterra Functional Integrodifferential Equations with Vanishing Linear Delays
Table 3
Comparison of the approximate solutions
āā
for
obtained by VIM and exact solution for Example
3.
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Exact solution
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| 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 |
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Exact solution | | | | | |
| 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 |
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