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Theory and Modern Applications

Table 2 The numerical verification of theoretical accuracy O( Ï„ 2 + h 4 )

From: High-order conservative Crank-Nicolson scheme for regularized long wave equation

 

∥ e n (h,τ)∥/∥ e 4 n ( h 2 , τ 4 )∥

∥ e n ( h , τ ) ∥ ∞ / ∥ e 4 n ( h 2 , τ 4 ) ∥ ∞

τ = 0.2, h = 0.1

τ = 0.05, h = 0.05

τ = 0.0125, h = 0.025

τ = 0.2, h = 0.1

τ = 0.05, h = 0.05

τ = 0.0125, h = 0.025

t = 2

-

15.940202

15.996241

-

15.935139

15.995926

t = 4

-

15.937612

15.996078

-

15.925675

15.995839

t = 6

-

15.934289

15.995869

-

15.929016

15.995554

t = 8

-

15.930779

15.995648

-

15.924811

15.995067

t = 10

-

15.927366

15.995430

-

15.917690

15.993525