Numerical Solution of In-Viscid Burger Equation in the Application of Physical Phenomena: The Comparison between Three Numerical Methods

Table 1

Comparison of point average absolute error, root mean square error, and pointwise maximum absolute error for problem give in example one with computations domain carried out until final time with different mesh size h and time step .

Applied numerical scheme	Specified mesh size		Estimated errors by using specified mesh size
	Upwind methods	0.025	0.01	2.5000E − 03		1.1291E − 03	5.1980 E − 04
0.0125		0.002	1.2500E − 03		3.5557E − 04	1.0230E − 04
0.01		0.01	1.0000E − 03		7.0898E − 4	5.0495E − 04
0.01		0.005	1.0000E − 03		5.0187E − 04	2.5373E − 04
Lax–Friedrichs scheme	0.025	0.01	2.5000E − 03		1.1117E − 03	5.5122E − 04
	0.0125	0.02	1.2500E − 03		3.4930E − 04	1.1185E − 04
	0.01	0.01	1.0000E − 03		7.0736E − 04	5.0775e − 04
	0.01	0.005	1.0000E − 03		4.9905E − 04	2.5837E − 04
Lax–Wendroff scheme	0.025	0.01	3.2196E − 04		1.3774E − 04	6.2141E − 05
	0.0125	0.02	1.7711E − 03		4.6476E − 04	1.3230E − 04
	0.01	0.01	1.1205E − 03		7.8888E − 04	5.5965E − 04
	0.01	0.005	1.2586E − 03		6.0864E − 04	3.0534E − 04