Theory and Modern Applications
Table 3 \(\varepsilon^{n}\) at \(t=t_{n}\) for different values of α with \(h=\frac{1}{10},\tau=\frac{1}{20}\)
From: A conservative difference scheme for the Riesz space-fractional sine-Gordon equation
t | α = 1.1 | α = 1.75 | α = 1.99 | α = 2.0 |
|---|---|---|---|---|
0 | 16.028375166427221 | 16.026853085312613 | 16.026621262922639 | 16.026614500015587 |
10 | 16.028375167453508 | 16.026853083065745 | 16.026621263595434 | 16.026614500665112 |
20 | 16.028375167026866 | 16.026853083341813 | 16.026621263623838 | 16.026614500693057 |
30 | 16.028375169429935 | 16.026853082109128 | 16.026621263611123 | 16.026614500697043 |
40 | 16.028375169276917 | 16.026853082184989 | 16.026621262942438 | 16.026614500697779 |
50 | 16.028375174037464 | 16.026853082023688 | 16.026621263929581 | 16.026614500697725 |
60 | 16.028375172694766 | 16.026853081374647 | 16.026621263991700 | 16.026614500697306 |
70 | 16.028375173733984 | 16.026853080731076 | 16.026621263988194 | 16.026614500697072 |
80 | 16.028375174760189 | 16.026853081190453 | 16.026621263850092 | 16.026614500696731 |
90 | 16.028375175956295 | 16.026853082788968 | 16.026621264363811 | 16.026614500696208 |
100 | 16.028375178909357 | 16.026853082989092 | 16.026621264523360 | 16.026614500696372 |
110 | 16.028375178244517 | 16.026853083445701 | 16.026621264528124 | 16.026614500695700 |
120 | 16.028375179698422 | 16.026853085066683 | 16.026621264471139 | 16.026614500695260 |
130 | 16.028375180814812 | 16.026853085383230 | 16.026621264061959 | 16.026614500694873 |
140 | 16.028375181940007 | 16.026853087126149 | 16.026621264895454 | 16.026614500694507 |
150-Ï„ | 16.028375183321515 | 16.026853087643513 | 16.026621264907444 | 16.026614500694265 |