Optimal Rate of Convergence for a Nonstandard Finite Difference Galerkin Method Applied to Wave Equation Problems

Table 1

NSFD method error in both 𝐿² and 𝐻¹-norms.

𝑀	𝐿^2-error	𝐻^1-error	Rate 𝐿^2	Rate 𝐻^1
10	3.800𝐸−3	1.67𝐸−2
15	1.700𝐸−3	1.110𝐸−2	1.983	1.0073
20	1.000𝐸−3	8.200𝐸−3	1.8445	0.9688
25	6.591𝐸−4	6.700𝐸−3	1.8678	1.0134
50	2.012𝐸−4	3.400𝐸−3	1.7119	0.9786
100	5.098𝐸−5	1.800𝐸−3	1.9806	0.9175