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

Table 8

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

(𝑥,𝑦)	𝑡=0.01		𝑡=0.5		𝑡=2
	𝑣^∗(𝑥,𝑦,𝑡)	|𝑣^∗−𝑣|	𝑣^∗(𝑥,𝑦,𝑡)	|𝑣^∗−𝑣|	𝑣^∗(𝑥,𝑦,𝑡)	|𝑣^∗−𝑣|
(0.1,0.1)	−0.003217063991	2𝐸−11	−0.003077270449	5𝐸−10	−0.002683638014	4𝐸−7
(0.5,0.1)	−4.350477708𝐸−20	4𝐸−20	−6.738702226𝐸−10	6𝐸−10	−4.937502413𝐸−6	4𝐸−6
(0.9,0.1)	−0.003859067764	1𝐸−9	0.003659637690	4𝐸−9	0.003090544099	2𝐸−5
(0.3,0.3)	−0.002534756956	0𝐸−0	−0.002447164709	5𝐸−10	−0.002188737874	2𝐸−6
(0.7,0.3)	0.005699386966	1𝐸−8	0.005274890097	2𝐸−8	0.004315287928	1𝐸−4
(0.1,0.5)	−0.0000000000	0𝐸−0	−0.0000000000	0𝐸−0	0.0000000000	0𝐸−0
(0.5,0.5)	0.0000000000	0𝐸−0	0.0000000000	0𝐸−0	0.0000000000	0𝐸−0
(0.9,0.5)	−0.0000000000	0𝐸−0	−0.0000000000	0𝐸−0	0.0000000000	0𝐸−0
(0.3,0.7)	0.002534756959	0𝐸−0	0.002447164718	5𝐸−10	0.002188737877	2𝐸−6
(0.7,0.7)	−0.005699453379	5𝐸−8	−0.005275019330	1𝐸−7	−0.004315322934	1𝐸−4
(0.1,0.9)	0.003217064054	9𝐸−11	0.003077270418	4𝐸−10	0.002683637890	4𝐸−7
(0.5,0.9)	4.350477662𝐸−20	4𝐸−20	6.738702149𝐸−10	6𝐸−10	4.937502361𝐸−6	4𝐸−6
(0.9,0.9)	−0.003859067867	1𝐸−9	−0.003659637235	4𝐸−9	−0.003090543816	2𝐸−5