Table 3 Analysis of the computational complexity
Approaches | Operation | Required flops \(\mathcal {O}\{\cdot \}\) |
|---|---|---|
WSFOPDE | Step 1 | \(\frac {1}{2}TM^{2} N^{2}\) |
Step 2 | M 3 N 3 | |
Step 3 | \((K_{1}+Q)(N-K)\left [7\left (K+1\right)^{2}+3K^{2}+\frac {5}{2}K+\frac {3}{2}\right ]\) | |
Step 4 | (K+1)3 | |
Step 5 | K[(M2N+M2)(MN−K1−Q)+M3] | |
\( M^{3}(N-K_{2})\left [N^{2}+2N(N-K_{2})+\left (N-K_{2}\right)^{2}\right ]+ M^{3}N^{3}+2K_{1}M^{2}N^{2} +2K_{1}^{2}MN+K_{1}^{3}\) | ||
Step 6 | K1[(M2N+M2)(MN−K1−Q)+M3] | |
Step 7 | 2M3N3 | |
\(\frac {1}{2}(N-Z_{1}+1)(M-Z_{2}+1)MN Z_{1}^{2}Z_{2}^{2} + Z_{1}^{3}Z_{2}^{3}\) | ||
Step 8 | \(K_{2} \left [Z_{2}^{2}(Z_{1}+1)(Z_{1}Z_{2}-K_{2})+Z_{2}^{3}\right ]\) | |
Improved WSFOPDE | Step 1 | \(\frac {1}{2}TM^{2} N^{2}\) |
Step 2 | M 3 N 3 | |
Step 3 | \((K_{1}+Q)(N-K)\left [7\left (K+1\right)^{2}+3K^{2}+\frac {5}{2}K+\frac {3}{2}\right ]\) | |
Step 4 | (K+1)3 | |
Step 5 | K1[(M2N+M2)(MN−K1−Q)+M3] | |
Step 6 | \(K_{1}{\bar {n}}_{1}\left [\left (M^{2}N+M^{2}\right)(MN-K_{1}-Q)+ M^{3}\right ]\) | |
\( M^{3}(N-K_{2})\left [N^{2}+2N(N-K_{2})+\left (N-K_{2}\right)^{2}\right ]+ M^{3}N^{3}+2K_{1}M^{2}N^{2} +2K_{1}^{2}MN+K_{1}^{3}\) | ||
Step 7 | K1[(M2N+M2)(MN−K1−Q)+M3] | |
Step 8 | 2M3N3 | |
\(\frac {1}{2}(N-Z_{1}+1)(M-Z_{2}+1)MN Z_{1}^{2}Z_{2}^{2} + Z_{1}^{3}Z_{2}^{3}\) | ||
Step 9 | \(K_{2}{\bar {n}}_{2}\left [Z_{2}^{2}(Z_{1}+1)(Z_{1}Z_{2}-K_{2})+Z_{2}^{3}\right ]\) | |
Step 10 | \(K_{2} \left [Z_{2}^{2}(Z_{1}+1)(Z_{1}Z_{2}-K_{2})+Z_{2}^{3}\right ]\) |