$\begin{split} &{p^{k + 1}}(i,j) \\= & \, 2{p^k}(i,j) - {p^{k - 1}}(i,j)\\ & + \frac{{{v^2}\Delta {t^2}}}{{\Delta {h^2}}}\left\{ { - \frac{1}{{560}}} \right.\left[ {{p^k}(i - 4,j) + {p^k}(i + 4,j)} \right]\\ & + \frac{8}{{315}}\left[ {{p^k}(i - 3,j) + {p^k}(i + 3,j)} \right]\\ & - \frac{1}{5}\left[ {{p^k}(i - 2,j) + {p^k}(i + 2,j)} \right]\\ & +\left. \frac{8}{5}\left[ {{p^k}(i - 1,j) + {p^k}(i + 1,j)} \right] - \frac{{205}}{{72}}{p^k}(i,j)\right\}\\ & + \frac{{{v^2}\Delta {t^2}}}{{\Delta {h^2}}}\left\{ { - \frac{1}{{560}}} \right.\left[ {{p^k}(i,j - 4) + {p^k}(i,j + 4)} \right]\\ & + \frac{8}{{315}}\left[ {{p^k}(i,j - 3) + {p^k}(i,j + 3)} \right]\\ & - \frac{1}{5}\left[ {{p^k}(i,j - 2) + {p^k}(i,j + 2)} \right]\\ & +\left. \frac{8}{5}\left[ {{p^k}(i,j - 1) + {p^k}(i,j + 1)} \right] - \frac{{205}}{{72}}{p^k}(i,j)\right\}\\ & + f(t) * \delta (i - {i_0}) * \delta (i - {j_0})\\ & i = 1,2, \cdots, nx - 1;j = 1,2, \cdots, \\ & ny - 1;k = 2,3, \cdots, nt \end{split}$![]() ![]() | (17) |