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

Table 3

Example 6.3: 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=3	𝛾=1	𝛾=2	𝛾=3
1/4 (CPU time)	0.4719E-03	0.9207E-04	0.2974E-04	0.8616E-03	0.7412E-03	0.4433E-04
	(0.2680)	(0.2530)	(0.2712)	(0.3322)	(0.3221)	(0.3476)
1/8 (CPU time)	0.3186E-04	0.7369E-05	0.2594E-06	0.5050E-04	0.4244E-04	0.2211E-05
	(3.0112)	(2.9443)	(2.9417)	(3.8616)	(3.7824)	(3.8806)
1/16 (CPU time)	0.2041E-05	0.4868E-06	0.1008E-07	0.3368E-05	0.2018E-05	0.1060E-06
	(49.9442)	(47.6788)	(49.0598)	(63.8846)	(62.1258)	(63.1625)
1/32 (CPU time)	0.1279E-06	0.3061E-07	0.6260E-09	0.2100E-06	0.1212E-06	0.6214E-08
	(703.2124)	(659.7450)	(685.7455)	(879.6670)	(825.1212)	(832.6086)