A New Efficient Method for Solving Two-Dimensional Burgers' Equation

Table 7

The LTNHPM results for 𝑢(𝑥,𝑦,𝑡) for the first five approximations with 𝑅=500.

(𝑥,𝑦)	𝑡=0.01		𝑡=0.5		𝑡=2
	𝑢^∗(𝑥,𝑦,𝑡)	|𝑢^∗−𝑢|	𝑢^∗(𝑥,𝑦,𝑡)	|𝑢^∗−𝑢|	𝑢^∗(𝑥,𝑦,𝑡)	|𝑢^∗−𝑢|
(0.1,0.1)	−0.002877429822	3𝐸−10	−0.002752396466	2𝐸−9	−0.002412373414	1𝐸−5
(0.5,0.1)	0.003879391382	0𝐸−0	0.003696240199	3𝐸−9	0.003158290011	2𝐸−5
(0.9,0.1)	−0.003451655816	3𝐸−10	−0.003273279771	3𝐸−9	−0.002774708749	1𝐸−5
(0.3,0.3)	0.002267155545	2𝐸−12	0.002188809320	1𝐸−9	0.001947448603	1𝐸−5
(0.7,0.3)	0.005097690552	5𝐸−9	0.004717986784	1𝐸−9	0.003624160352	1𝐸−4
(0.1,0.5)	−0.007851234710	2𝐸−12	−0.007561582238	1𝐸−8	−0.006599038031	1𝐸−4
(0.5,0.5)	0.01255397423	1𝐸−11	0.01196126856	2𝐸−8	0.01020345914	1𝐸−4
(0.9,0.5)	−0.01437772613	1𝐸−8	−0.01343545467	1𝐸−7	−0.01201493924	1𝐸−3
(0.3,0.7)	0.002267155545	3𝐸−12	0.002188809324	1𝐸−9	0.001947448606	1𝐸−5
(0.7,0.7)	0.005097745644	4𝐸−8	0.004718074710	8𝐸−8	0.003624161959	1𝐸−4
(0.1,0.9)	−0.002877429571	9𝐸−11	−0.002752396375	2𝐸−9	−0.002412373226	1𝐸−5
(0.5,0.9)	0.003879391372	0𝐸−0	0.0036962440189	4𝐸−9	0.003158290003	2𝐸−5
(0.9,0.9)	−0.003451655844	3𝐸−9	−0.003273279804	3𝐸−9	−0.002774708685	1𝐸−5