From: A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline
Time | \({I_{1}}\) | \({I_{2}}\) | \({I_{3}}\) | ||||||
---|---|---|---|---|---|---|---|---|---|
pĀ =Ā 2 | pĀ =Ā 3 | pĀ =Ā 4 | pĀ =Ā 2 | pĀ =Ā 3 | pĀ =Ā 4 | pĀ =Ā 2 | pĀ =Ā 3 | pĀ =Ā 4 | |
Our results for \({U_{0}}=0.1,x_{0}=0,d=5,\mu =1/6,h=0.1,{\Delta{t}}=0.1,x\in \left[ -36,300\right] \) | |||||||||
0 | 3.5949 | 3.5949 | 3.5949 | 0.3344 | 0.3344 | 0.3344 | 0.0031 | 0.0031 | 0.0031 |
50 | 3.6051 | 3.6050 | 3.6049 | 0.3348 | 0.3350 | 0.3350 | 0.0019 | 0.0016 | 0.0015 |
100 | 3.6051 | 3.6050 | 3.6050 | 0.3348 | 0.3350 | 0.3350 | 0.0018 | 0.0016 | 0.0015 |
150 | 3.6050 | 3.6050 | 3.6049 | 0.3350 | 0.3349 | 0.3350 | 0.0017 | 0.0016 | 0.0015 |
200 | 3.6050 | 3.6050 | 3.6049 | 0.3354 | 0.3349 | 0.3350 | 0.0012 | 0.0016 | 0.0015 |
Time | \({I_{1}}\) | \({I_{2}}\) | \({I_{3}}\) | ||||||
---|---|---|---|---|---|---|---|---|---|
pĀ =Ā 2 | Ā | Ā | pĀ =Ā 2 | Ā | Ā | pĀ =Ā 2 | Ā | Ā | |
QBSC[28] results for \({U_{0}}=0.1,d=5,\mu =3/2,h=0.2,{\Delta{t}}=0.1,x\in \left[ 0,250\right] \) | |||||||||
0 | 4.0000 | Ā | Ā | 0.3759 | Ā | Ā | 0.0025 | Ā | Ā |
50 | 4.8507 | Ā | Ā | 0.4620 | Ā | Ā | 0.0034 | Ā | Ā |
100 | 5.7016 | Ā | Ā | 0.5480 | Ā | Ā | 0.0042 | Ā | Ā |
150 | 6.5531 | Ā | Ā | 0.6341 | Ā | Ā | 0.0051 | Ā | Ā |
200 | 7.4055 | Ā | Ā | 0.7204 | Ā | Ā | 0.0060 | Ā | Ā |