Research Article

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

Table 7

Order of convergence.

ExampleParametersOrder of the method

01 𝛼 = 1 0 , 𝛽 = 5 , 𝜂 = 0 . 5 , 𝛾 = 1 at 𝑡 = 5 4.00
𝛼 = 2 0 , 𝛽 = 1 0 , 𝜂 = 1 , 𝛾 = 1 at 𝑡 = 5 4.02
𝛼 = 4 0 , 𝛽 = 4 , 𝜂 = 1 0 , 𝛾 = 2 0 at 𝑡 = 5 3.99
𝛼 = 5 0 , 𝛽 = 5 , 𝜂 = 0 . 2 5 , 𝛾 = 0 . 7 5 at 𝑡 = 5 3.99
𝛼 = 1 0 , 𝛽 = 0 , 𝜂 = 5 , 𝛾 = 5 at 𝑡 = 5 4.00

02at 𝑡 = 1 4.00
at 𝑡 = 2 3.99

03 𝛾 = 1 at 𝑡 = 2 3.99
𝛾 = 2 at 𝑡 = 2 3.99
𝛾 = 3 at 𝑡 = 2 4.00

04 𝑡 = 1 3.99

05 𝛾 = 1 at 𝑡 = 1 4.00
𝛾 = 2 at 𝑡 = 1 3.99
𝛾 = 5 at 𝑡 = 1 4.01

06 𝛾 = 1 at 𝑡 = 1 4.00
𝛾 = 2 at 𝑡 = 1 4.01
γ=5 at 𝑡 = 1 4.00