An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 14 Comparison of the values of \(Y(\xi , \eta , t)\) and \(Z(\xi , \eta , t)\) of Example 8 for \(T=0.01\) using regular points

Points	Present method		[49]		[4]
	N = 100	N = 400	N = 100	N = 400	N = 100	N = 400
	dt = 0.0002	0.0001	dt = 0.0002	0.0001	dt = 0.00125	–
solution of Y
(0.1,0.1)	0.07299	0.07260	0.07279	0.07257	0.07254	0.07251
(0.2,0.8)	0.28886	0.28861	0.28867	0.28842	0.27778	0.27778
(0.4,0.4)	0.72340	0.72256	0.72375	0.7221	0.72174	0.72174
(0.7,0.1)	0.20148	0.20125	0.20157	0.20117	0.20481	0.20484
(0.9,0.9)	0.07939	0.07945	0.07951	0.07947	0.07942	0.07944
solution of Z
(0.1,0.1)	0.43027	0.43239	0.44132	0.44336	0.43159	0.43087
(0.2,0.8)	−0.1242	−0.1225	−0.13172	−0.12366	−0.12428	−0.1241
(0.4,0.4)	1.65850	1.65514	1.66212	1.65499	1.65245	1.65244
(0.7,0.1)	0.06571	0.06662	0.06306	0.06621	0.06716	0.06705
(0.9,0.9)	0.01212	0.01364	0.01459	0.01367	0.01358	0.01335