A New Approach to Numerical Solution of Nonlinear Klein-Gordon Equation

Table 1

𝐿_∞,𝐿₂, and RMS errors of Example 2 for 𝑁=4 and ℎ=0.1.

𝑡	𝐿∞-error	𝐿2-error	RMS-error
0	0	0	0
0.1	4.9593𝐸−8	9.6138𝐸−6	2.8986𝐸−6
0.2	5.6542𝐸−7	5.4883𝐸−6	1.6532𝐸−6
0.3	1.8493𝐸−6	1.1933𝐸−5	3.5979𝐸−6
0.4	3.2841𝐸−6	1.5829𝐸−5	4.7726𝐸−6
0.5	3.8373𝐸−6	1.4683𝐸−5	4.4271𝐸−6
0.6	4.6197𝐸−6	1.4714𝐸−5	4.4366𝐸−6
0.7	1.4141𝐸−5	3.9360𝐸−5	1.1867𝐸−5
0.8	5.6879𝐸−5	1.3952𝐸−4	4.2069𝐸−5
0.9	1.8571𝐸−4	4.0542𝐸−4	1.2224𝐸−4
1	2.2334𝐸−4	9.7993𝐸−4	2.9546𝐸−4