Advances in Mathematical Physics

Research Article

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

Table 2

Example 6.2: the maximum absolute errors (with CPU time).
ℎ Proposed 𝑂 ( 𝑘 2 + 𝑘 2 ℎ 2 + ℎ 4 ) -method 𝑂 ( 𝑘 4 + 𝑘 2 ℎ 2 + ℎ 4 ) -method discussed in [6]
𝑡 = 1 𝑡 = 2 𝑡 = 1 𝑡 = 2
1 / 8 (CPU time) 0 . 1 0 7 3 E - 0 5 0 . 7 8 8 3 E - 0 6 0 . 8 7 8 2 E - 0 5 0 . 7 2 6 0 E - 0 5
(0.1077)(0.1488)(0.1344)(0.1985)
1 / 1 6 (CPU time) 0 . 6 0 2 6 E - 0 7 0 . 5 4 2 4 E - 0 7 0 . 4 8 8 8 E - 0 6 0 . 3 8 4 2 E - 0 6
(0.6614)(1.2736)(1.0404)(1.6892)
1 / 3 2 (CPU time) 0 . 4 6 2 6 E - 0 8 0 . 4 5 3 3 E - 0 8 0 . 2 7 1 8 E - 0 7 0 . 2 1 4 6 E - 0 7
(9.2670)(16.4166)(12.8822)(20.3392)
1 / 6 4 (CPU time) 0 . 2 8 9 2 E - 0 9 0 . 2 8 6 4 E - 0 9 0 . 1 6 1 6 E - 0 8 0 . 1 2 8 4 E - 0 8
(142.9786)(300.5124)(178.3944)(380.6638)