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

Table 5

Example 6.5: 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 [6]
	𝛾=1	𝛾=2	𝛾=5	𝛾=1	𝛾=2	𝛾=5
1/4 (CPU time)	0.1067E-03	0.3903E-03	0.8100E-02	0.7776E-03	0.9220E-03	0.2318E-01
	(0.2404)	(0.2493)	(0.2482)	(0.3002)	(0.3122)	(0.3120)
1/8 (CPU time)	0.9365E-05	0.3437E-04	0.6271E-03	0.4418E-04	0.6072E-04	0.1272E-02
	(1.6889)	(1.7670)	(2.0218)	(2.1122)	(2.2424)	(2.5560)
1/16 (CPU time)	0.6667E-06	0.2416E-05	0.4248E-04	0.2218E-05	0.3664E-05	0.8814E-04
	(25.9590)	(27.6302)	(32.5906)	(31.0244)	(33.4255)	(40.1616)
1/32 (CPU time)	0.4148E-07	0.1523E-06	0.2608E-05	0.1360E-06	0.2214E-06	0.5416E-05
	(367.1442)	(396.0654)	(455.2458)	(459.1677)	(495.8262)	(569.1088)