Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs

Table 2

The error and convergence orders of (3.21) for Klein-Gordon problem with Δ𝑡=Δ𝑥.

Mesh size	𝑡=1	𝑡=1.5	𝑡=2
Δ𝑥=0.1
Error	1.28𝑒−2	1.81𝑒−2	2.25𝑒−2
Order	—	—	—
Δ𝑥=0.05
Error	3.3𝑒−3	4.6𝑒−3	5.7𝑒−3
Order	1.9556	1.9763	1.9809
Δ𝑥=0.025
Error	8.3445𝑒−4	1.2𝑒−3	1.4𝑒−3
Order	1.9836	1.9386	2.0255
Δ𝑥=0.0125
Error	2.0990𝑒−4	2.9458𝑒−4	3.6187𝑒−4
Order	1.9911	2.0263	1.9984