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

Table 1

Example 6.1: the maximum absolute errors (using proposed 𝑂(𝑘²+𝑘²ℎ²+ℎ⁴)-method) (with CPU time).

ℎ	𝛼=10, 𝛽=5, 𝜂=0.5, 𝛾=1	𝛼=20, 𝛽=10, 𝜂=1, 𝛾=1	𝛼=40, 𝛽=4, 𝜂=10, 𝛾=20	𝛼=50, 𝛽=5, 𝜂=0.25, 𝛾=0.75	𝛼=10, 𝛽=0, 𝜂=5, 𝛾=5
1/8 (CPU time)	0.5800E-07; (0.2087)	0.1784E-06; (0.2781)	0.4051E-02; (0.2084)	0.1119E-04; (0.2214)	0.6781E-04; (0.2120)
	^∗0.9234E-07; (0.2548)	^∗0.6873E-06; (0.3442)	^∗0.6677E-02; (0.2526)	^∗0.8820E-04; (0.2610)	^∗0.8873E-04; (0.2566)
1/16 (CPU time)	0.2390E-08; (1.9938)	0.2318E-08; (2.0041)	0.1930E-03; (1.9580)	0.6200E-06; (1.9844)	0.3125E-05; (1.9636)
	^∗0.6894E-08; (2.3690)	^∗0.8329E-08; (2.4715)	^∗0.3210E-03; (2.3427)	^∗0.5033E-05; (2.3677)	^∗0.5012E-05; (2.3525)
1/32 (CPU time)	0.1450E-09; (30.9160)	0.1132E-09; (31.1875)	0.1178E-04; (30.8334)	0.3899E-07; (31.2224)	0.1917E-06; (31.2644)
	^∗0.3634E-09; (38.8461)	^∗0.4418E-09; (39.1400)	^∗0.2144E-04; (38.3874)	^∗0.2482E-06; (39.3487)	^∗0.2898E-06; (39.9912)
1/64 (CPU time)	0.9055E-11; (493.5212)	0.6948E-11; (503.4469)	0.7365E-06; (492.8654)	0.2439E-08; (498.1166)	0.1198E-07; (500.2034)
	^∗0.2239E-10; (602.1290)	^∗0.2746E-10; (620.2021)	^∗0.1312E-05; (601.6682)	^∗0.1419E-07; (611.8769)	^∗0.1767E-07; (616.1248)

∗Result obtained by using the Method discussed in [13].