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

Table 2

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

(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)	0.8750097656	9𝐸−6	0.8754882787	4𝐸−4	0.8769525545	1𝐸−3
(0.5,0.1)	0.8765721828	1𝐸−3	0.8770505973	2𝐸−3	0.8785142944	3𝐸−3
(0.9,0.1)	0.8781341113	3𝐸−3	0.8786122779	3𝐸−3	0.8800749409	5𝐸−3
(0.3,0.3)	0.8750097656	9𝐸−6	0.8754882787	4𝐸−4	0.8769525545	1𝐸−3
(0.7,0.3)	0.8765721828	1𝐸−3	0.8770505973	2𝐸−3	0.8785142944	3𝐸−3
(0.1,0.5)	0.8734473429	1𝐸−3	0.8739258051	1𝐸−3	0.8753902032	3𝐸−4
(0.5,0.5)	0.8750097656	9𝐸−6	0.8754882787	4𝐸−4	0.8769525545	1𝐸−3
(0.9,0.5)	0.8765721828	1𝐸−3	0.8770505973	2𝐸−3	0.8785142944	3𝐸−3
(0.3,0.7)	0.8734473429	1𝐸−3	0.8739258051	1𝐸−3	0.8753902032	3𝐸−4
(0.7,0.7)	0.8750097656	9𝐸−6	0.8754882787	4𝐸−4	0.8769525545	1𝐸−3
(0.1,0.9)	0.8753902032	3𝐸−3	0.8723636741	2𝐸−3	0.8738277383	1𝐸−3
(0.5,0.9)	0.8734473429	3𝐸−10	0.8739258051	1𝐸−3	0.8753902032	3𝐸−4
(0.9,0.9)	0.8750097656	1𝐸−3	0.8754882787	4𝐸−4	0.8769525545	1𝐸−3