Table 1 Comparison between LRPSM with FTC-VIM and FTC-HPM for example 1.
From: Adapting Laplace residual power series approach to the Caudrey Dodd Gibbon equation
x | t | Numerical solution | |||||
|---|---|---|---|---|---|---|---|
LRPSM with 3 terms | LRPSM with 2 terms | FTC-VIM37 | FTC-HPM37 | ||||
α = 0.7 | α = 0.9 | α = 1 | α = 1 | α = 1 | α = 1 | ||
-50 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 6.40972e−14 | 1.87107e−14 | 3.78100e−16 | 1.80551e−14 | 1.76778e−11 | 1.76778e−11 | |
4 | 3.04059e−13 | 1.07794e−13 | 2.97855e−15 | 7.07545e−14 | 3.53211e−11 | 3.53211e−11 | |
6 | 5.67030e−13 | 2.13785e−13 | 9.90035e−15 | 1.55999e−13 | 5.29318e−11 | 5.29318e−11 | |
8 | 8.32476e−13 | 3.27108e−13 | 2.31153e−14 | 2.71817e−13 | 7.05119e−11 | 7.05119e−11 | |
10 | 1.09255e−12 | 4.43976e−13 | 4.44757e−14 | 4.16356e−13 | 8.80633e−11 | 8.80633e−11 | |
-40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 9.51288e−12 | 2.77692e−12 | 5.61150e−14 | 2.67962e−12 | 2.62363e−09 | 2.62363e−09 | |
4 | 4.51263e−11 | 1.59981e−11 | 4.42056e−13 | 1.05009e−11 | 5.24212e−09 | 5.24212e−09 | |
6 | 8.41547e−11 | 3.17285e−11 | 1.469342e−12 | 2.31523e−11 | 7.85578e−09 | 7.85578e−09 | |
8 | 1.23550e−10 | 4.85472e−11 | 3.43061e−12 | 4.03412e−11 | 1.04649e−08 | 1.04649e−08 | |
10 | 1.62149e−10 | 6.58920e−11 | 6.60078e−12 | 6.17927e−11 | 1.30697e−08 | 1.30697e−08 | |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 1.50403e−04 | 4.18130e−05 | 1.26391e−06 | 1.85127e−05 | 6.54334e−02 | 6.54334e−02 | |
4 | 7.46909e−04 | 2.52505e−04 | 1.01620e−05 | 7.91573e−05 | 1.30909e−01 | 1.30909e−01 | |
6 | 1.41638e−03 | 4.96853e−04 | 3.44342e−05 | 1.89673e−04 | 1.96434e−01 | 1.96434e−01 | |
8 | 2.09931e−03 | 7.42150e−04 | 8.18630e−05 | 3.57844e−04 | 2.62018e−01 | 2.62018e−01 | |
10 | 2.76599e−03 | 9.68940e−04 | 1.60187e−04 | 5.91408e−04 | 3.27666e−01 | 3.27666e−01 | |
40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 1.24156e−12 | 3.47519e−13 | 7.83542e−15 | 3.78077e−13 | 4.02445e−10 | 4.02445e−10 | |
4 | 6.99716e−12 | 2.45302e−12 | 6.36846e−14 | 1.54465e−12 | 8.04102e−10 | 8.04102e−10 | |
6 | 1.44110e−11 | 5.42196e−12 | 2.18401e−13 | 3.55058e−12 | 1.20491e−09 | 1.20491e−09 | |
8 | 2.3152e−11 | 9.15479e−12 | 5.26119e−13 | 6.44999e−12 | 1.60484e−09 | 1.60484e−09 | |
10 | 3.31208e−11 | 1.36464e−11 | 1.04446e−12 | 1.03005e−11 | 2.00381e−09 | 2.00381e−09 | |
50 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 8.36560e−15 | 2.34156e−15 | 5.27946e−17 | 2.54746e−15 | 2.71165e−12 | 2.71165e−12 | |
4 | 4.71465e−14 | 1.65283e−14 | 4.29103e−16 | 1.04077e−14 | 5.41799e−12 | 5.41799e−12 | |
6 | 9.71007e−14 | 3.65329e−14 | 1.47157e−15 | 2.39236e−14 | 8.11868e−12 | 8.11868e−12 | |
8 | 1.55998e−13 | 6.16844e−14 | 3.54496e−15 | 4.34597e−14 | 1.08133e−11 | 1.08133e−11 | |
10 | 2.23166e-13 | 9.19492e-14 | 7.03753e-15 | 6.94043e-14 | 1.35016e-11 | 1.35016e-11 | |
