Exact finite-difference scheme and nonstandard finite-difference scheme for coupled Burgers equation

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 The numerical results of first scheme ( 46 ) and second scheme ( 47 ) for v with the exact solution at $t = 0.01$ , $t = 0.5$ and $t = 2$ with $t = 0.0001$ , and $R = 10$

(x,y)	t = 0.01			t = 0.5			t = 2
(x,y)	First	Second	Exact	First	Second	Exact	First	Second	Exact
(0.1,0.1)	0.87519	0.87519	0.87520	0.88471	0.88472	0.88475	0.91280	0.91282	0.91284
(0.5,0.1)	0.90579	0.90579	0.90580	0.91454	0.91456	0.91460	0.93866	0.93870	0.93873
(0.9,0.1)	0.93291	0.93292	0.93292	0.94011	0.94014	0.94016	0.95883	0.95886	0.95887
(0.3,0.3)	0.87519	0.87519	0.87520	0.88461	0.88462	0.88475	0.91268	0.91275	0.91284
(0.7,0.3)	0.90579	0.90579	0.90580	0.91442	0.91449	0.91460	0.93853	0.93864	0.93873
(0.1,0.5)	0.84456	0.84456	0.84457	0.85366	0.85365	0.85372	0.88272	0.88274	0.88280
(0.5,0.5)	0.87519	0.87519	0.87520	0.88452	0.88454	0.88475	0.91255	0.91266	0.91284
(0.9,0.5)	0.90579	0.90579	0.90580	0.91444	0.91449	0.91460	0.93854	0.93864	0.93873
(0.3,0.7)	0.84456	0.84456	0.84457	0.85357	0.85352	0.85372	0.88257	0.88261	0.88280
(0.7,0.7)	0.87519	0.87519	0.87520	0.88449	0.88450	0.88475	0.91247	0.91260	0.91284
(0.1,0.9)	0.81739	0.81738	0.81739	0.82515	0.82512	0.82519	0.85178	0.85177	0.85183
(0.5,0.9)	0.84456	0.84456	0.84457	0.85358	0.85353	0.85372	0.88256	0.88260	0.88280
(0.9,0.9)	0.87519	0.87519	0.87520	0.88462	0.88463	0.88475	0.91266	0.91272	0.91284