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

Table 1

The LTNHPM results for 𝑢(𝑥,𝑦,𝑡) for the first five approximations with 𝑅=0.5.

(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)	0.6249902344	9𝐸−6	0.6245117213	4𝐸−4	0.6230474455	1𝐸−3
(0.5,0.1)	0.6234278173	9𝐸−6	0.6229494028	2𝐸−3	0.6214857057	3𝐸−3
(0.9,0.1)	0.6218658937	3𝐸−3	0.6213877271	3𝐸−3	0.6199250641	5𝐸−3
(0.3,0.3)	0.6249902344	9𝐸−6	0.6245117213	4𝐸−4	0.6230474455	1𝐸−3
(0.7,0.3)	0.6234278173	1𝐸−3	0.6229494028	2𝐸−3	0.6214857057	3𝐸−3
(0.1,0.5)	0.6265526528	1𝐸−3	0.6260741906	1𝐸−3	0.6246097925	3𝐸−4
(0.5,0.5)	0.6249902344	9𝐸−6	0.6245117213	4𝐸−4	0.6230474455	3𝐸−3
(0.9,0.5)	0.6234278173	1𝐸−3	0.6229494028	2𝐸−3	0.6214857057	3𝐸−3
(0.3,0.7)	0.6265526528	1𝐸−3	0.6260741906	1𝐸−3	0.62460987925	3𝐸−4
(0.7,0.7)	0.6249902344	9𝐸−6	0.6245117213	4𝐸−4	0.6230474455	1𝐸−3
(0.1,0.9)	0.6281145910	3𝐸−3	0.6276363292	2𝐸−3	0.6261722650	1𝐸−3
(0.5,0.9)	0.6265526528	1𝐸−3	0.6260741906	1𝐸−3	0.6246097925	3𝐸−3
(0.9,0.9)	0.6249902344	9𝐸−6	0.6245117213	4𝐸−4	0.6230474455	1𝐸−3