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

Table 2

Absolute errors of Example 3 for 𝑁=4.

𝑡	𝑡=0.001		𝑡=0.01		𝑡=0.1
𝑥𝑖	𝑐=0.01	𝑐=0.05	𝑐=0.01	𝑐=0.05	𝑐=0.01	𝑐=0.05
0.1	5.13𝐸−9	5.19𝐸−9	6.18𝐸−7	5.20𝐸−7	5.88𝐸−5	5.91𝐸−5
0.2	9.58𝐸−6	9.61𝐸−6	9.39𝐸−6	9.42𝐸−6	1.63𝐸−5	1.63𝐸−5
0.3	3.67𝐸−6	3.68𝐸−6	3.67𝐸−6	3.68𝐸−6	1.20𝐸−6	2.91𝐸−6
0.4	2.68𝐸−6	2.69𝐸−6	2.61𝐸−6	2.62𝐸−6	2.42𝐸−6	1.23𝐸−6
0.4	3.66𝐸−6	3.67𝐸−6	3.60𝐸−6	3.61𝐸−6	3.69𝐸−6	2.47𝐸−6
0.5	3.91𝐸−11	4.61𝐸−6	2.02𝐸−9	2.19𝐸−6	5.18𝐸−6	3.76𝐸−6
0.6	3.84𝐸−6	3.86𝐸−6	3.78𝐸−6	3.79𝐸−6	6.85𝐸−6	5.28𝐸−6
0.7	2.96𝐸−6	2.97𝐸−6	2.87𝐸−6	2.88𝐸−6	4.65𝐸−6	7.00𝐸−6
0.8	4.26𝐸−6	4.27𝐸−6	1.14𝐸−6	1.12𝐸−5	1.39𝐸−5	1.37𝐸−5
0.9	1.16𝐸−5	1.17𝐸−5	4.27𝐸−6	3.63𝐸−6	7.51𝐸−5	7.36𝐸−5
1	6.90𝐸−9	9.88𝐸−5	1.16𝐸−7	2.68𝐸−6	1.39𝐸−5	1.44𝐸−5