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

Table 4

Comparison of the absolute errors for 𝑞=0.5,0.9 for Example 3.

𝑡	Exact solution; exp(−𝑡)	𝑞=0.5
		𝑒1(𝑡)	𝑒2(𝑡)	𝑒3(𝑡)	𝑒4(𝑡)
0.0	1	0	0	0	0
0.1	0.9048374181	1.4200646475443594𝑒−4	6.937511313111𝑒−8	1.646180933𝑒−11	2.43155𝑒−15
0.2	0.8187307531	1.10666495797771448𝑒−3	2.18076562663748𝑒−6	2.07892070592𝑒−9	1.15888751𝑒−12
0.3	0.7408182207	3.63975574333994118𝑒−3	1.627081685960135𝑒−5	3.504952023246𝑒−8	4.407648389𝑒−11
0.4	0.6703200461	8.41070704234255791𝑒−3	6.738054376503324𝑒−5	2.5912707216746𝑒−7	5.8081277444𝑒−10
0.5	0.6065306597	1.602012335877144465𝑒−2	2.0211666017597282𝑒−4	1.21953956992926𝑒−6	4.28195369561𝑒−9
0.6	0.5488116361	2.700658458769143342𝑒−2	4.9443661433166875𝑒−4	4.31350551554875𝑒−6	2.186375878938𝑒−8
0.7	0.4965853038	4.185278592730391965𝑒−2	1.05082474616155665𝑒−3	1.252782320403843𝑒−5	8.664290677367𝑒−8
0.8	0.4493289641	6.099108191841770932𝑒−2	2.01492041571414432𝑒−3	3.149838214027765𝑒−5	2.8522174369098𝑒−7
0.9	0.4065696598	8.480849188117418127𝑒−2	3.57165301825918244𝑒−3	7.093743332206066𝑒−5	8.1491443912479𝑒−7
1.0	0.3678794412	1.1365121854119110200𝑒−1	5.95093343943865667𝑒−3	1.46469545893926𝑒−4	2.08218958401362𝑒−6
𝑡	Exact solution	𝑞=0.9
		𝑒1(𝑡)	𝑒2(𝑡)	𝑒3(𝑡)	𝑒4(𝑡)
0.0	1	0	0	0	0
0.1	0.9048374181	9.657378138941948𝑒−5	3.270513490973𝑒−8	5.74139096𝑒−12	6.2728𝑒−16
0.2	0.8187307531	7.5269770605815316𝑒−4	1.02756966760297𝑒−6	7.2447942848𝑒−10	3.1746709𝑒−13
0.3	0.7408182207	2.47594283875612598𝑒−3	7.66325510054132𝑒−6	1.220476554969𝑒−8	1.206307741𝑒−11
0.4	0.6703200461	5.72235733715573104𝑒−3	3.172132588210038𝑒−5	9.016329013769𝑒−8	1.5881468019𝑒−10
0.5	0.6065306597	1.090164674390729482𝑒−2	9.511362494392321𝑒−5	4.2402608794109𝑒−7	1.16979520844𝑒−9
0.6	0.5488116361	1.838183744707893682𝑒−2	2.3258709410406167𝑒−4	1.49870662825066𝑒−6	5.96780575716𝑒−9
0.7	0.4965853038	2.849347454575559058𝑒−2	4.9413985645739533𝑒−4	4.34971803645698𝑒−6	2.362943512914𝑒−8
0.8	0.4493289641	4.153340030498488082𝑒−2	9.4717887892489095𝑒−4	1.092904838051250𝑒−5	7.772159979916𝑒−8
0.9	0.4065696598	5.776815482770151840𝑒−2	1.67844639226603561𝑒−3	2.459729456944614𝑒−5	2.2187992678186𝑒−7
1.0	0.3678794412	7.743703646222385168𝑒−2	2.79573942676327664𝑒−3	5.075582693458194𝑒−5	5.6647549440028𝑒−7