Skip to main content

Theory and Modern Applications

Table 1 Order of convergence

From: A new spline in compression method of order four in space and two in time based on half-step grid points for the solution of the system of 1D quasi-linear hyperbolic partial differential equations

Problem no.

Parameters and time

Order

6.1

\(\alpha_{0} = 12\), \(\beta_{0}=8\), η = γ = 1, t = 1, σ = 3.2

3.9834

\(\alpha_{0} = \beta_{0} = \pi\), η = 0.75, γ = 1.5, t = 1, σ = 3.2

4.0000

\(\alpha_{0} = 3\pi\), \(\beta_{0} = \pi\), η = 2.5, γ = 0.25, t = 1, σ = 3.2

3.9932

6.2

σ = 0.8, ε = 0.01, t = 1

4.0017

σ = 0.8, ε = 0.01, t = 2

4.0017

σ = 0.8, ε = 0.001, t = 1

4.0017

σ = 0.8, ε = 0.001, t = 2

4.0016

6.3

γ = 0.5, t = 1, σ = 3.2

3.9967

γ = 2, t = 1, σ = 3.2

3.9944

6.4

γ = 2, t = 1, σ = 3.2

4.0429

γ = 20, t = 1, σ = 3.2

3.9492

6.5

α = 0.5, t = 1, σ = 1.6

3.9399

α = 0.05, t = 1, σ = 1.6

3.9987