On the rate of convergence of the Legendre spectral collocation method for multi-dimensional nonlinear Volterra-Fredholm integral equations
Nermeen A Elkot,Mahmoud A Zaky,Eid H Doha,Ibrahem G Ameen
Table 1.
The
L
2
- errors for example
1
versus
N
.
Method [
31
]
Method [
30
]
Method [
6
]
Present method
n
,
m
$\parallel E\parallel $
2
M
$\parallel E\parallel $
n
,
m
$\parallel E\parallel $
N
$\parallel E\parallel $
2, 24
4.3 × 10
−3
4
1.3 × 10
−2
2, 4
9.1 × 10
−3
4
6.6 × 10
−5
4, 16
3.6 × 10
−4
8
6.1 × 10
−3
4, 4
2.1 × 10
−4
6
2.4 × 10
−7
4, 24
2.0 × 10
−4
16
8.8 × 10
−4
2, 8
7.5 × 10
−6
8
5.2 × 10
−10
10, 12
8.1 × 10
−6
32
9.8 × 10
−5
4, 8
1.6 × 10
−7
10
7.4 × 10
−13
10, 24
7.9 × 10
−7
64
4.2 × 10
−6
4, 16
5.0 × 10
−9
12
7.4 × 10
−16