Boundary conditions ( $i=0,n$ , $j=1,2,\cdots ,m$ ) $u\left(0,j\right)=0$ , $u\left(n,j\right)=0$ Initial Conditions ( $i=1,2,\cdots ,n-1$ , $j=0$ ) $\begin{array}{l}-2\omega r{u}_{i-1,1}+2\left(1+2\omega r\right){u}_{i,1}-2\omega r{u}_{i+1,1}\\ =\left(1-2\omega \right)r{u}_{i-1,0}+\left(2+4\omega r-2r\right){u}_{i,0}+\left(1-2\omega \right)r{u}_{i+1,0}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{ }-2\omega kr{g}_{i-1}+2\left(1-2\omega r\right)k{g}_{i}-2\omega kr{g}_{i+1}\end{array}$ (CD) (32) or $\begin{array}{l}-\omega r{u}_{i-1,1}+\left(1-2\omega r\right){u}_{i,1}-\omega r{u}_{i+1,1}\\ =\left(1-\omega \right)r{u}_{i-1,0}+\left(1+2\omega r-2r\right){u}_{i,0}+\left(1-\omega \right)r{u}_{i+1,0}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\omega kr\left(-{g}_{i-1}+2{g}_{i}-{g}_{i+1}\right)+\frac{1}{2}\omega {c}^{2}{k}^{2}r\left({{f}^{″}}_{i-1}-2{{f}^{″}}_{i}+{{f}^{″}}_{i}\right)+k{g}_{i}-\frac{1}{2}{c}^{2}{k}^{2}{{f}^{″}}_{i}\end{array}$ (BD) (33) or ${u}_{i,1}={f}_{i}+k{g}_{i}+\frac{1}{2}{k}^{2}{c}^{2}{{f}^{″}}_{i}$ (FD) (34) Rest Values ( $i=1,2,\cdots ,n-1$ , $j=1,2,\cdots ,m$ ) $\begin{array}{l}-\omega r{u}_{i-1,j+1}+\left(1+2\omega r\right){u}_{i,j+1}-\omega r{u}_{i+1,j+1}\\ =\left(1-2\omega \right)r{u}_{i-1,j}+\left(2+4\omega r-2r\right){u}_{i,j}+\left(1-2\omega \right)r{u}_{i+1,j}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{ }+\omega r{u}_{i-1,j-1}+\left(-1-2\omega r\right){u}_{i,j-1}+\omega r{u}_{i+1,j-1}\end{array}$ (35)