A New High-Order Approximation for the Solution of Two-Space-Dimensional Quasilinear Hyperbolic Equations

Table 6

Example 6.6: The maximum absolute errors (with CPU time).

ℎ	Proposed 𝑂(𝑘^2+𝑘^2ℎ^2+ℎ^4)-method			𝑂(𝑘^4+𝑘^2ℎ^2+ℎ^4)-method discussed in [7]
	𝛾=1	𝛾=2	𝛾=5	𝛾=1	𝛾=2	𝛾=5
1/4 (CPU time)	0.1286E-03	0.1251E-03	0.3733E-03	0.6618E-03	0.7715E-03	0.8812E-03
	(0.2602)	(0.2607)	(0.2532)	(0.3288)	(0.3292)	(0.3166)
1/8 (CPU time)	0.9423E-05	0.8670E-05	0.2271E-04	0.3336E-04	0.4112E-04	0.5080E-04
	(1.9640)	(1.9835)	(1.9870)	(2.3361)	(2.3410)	(2.3422)
1/16 (CPU time)	0.6313E-06	0.5622E-06	0.1452E-05	0.2112E-05	0.2446E-05	0.2863E-05
	(30.0540)	(29.7286)	(32.0085)	(37.6212)	(37.2268)	(40.1020)
1/32 (CPU time)	0.3939E-07	0.3490E-07	0.9018E-07	0.1308E-06	0.1512E-06	0.1744E-06
	(414.6224)	(405.4874)	(450.4474)	(517.6668)	(507.6543)	(563.5578)