Exact(1)
Applying the above approximation and impose them to the original Eq. (1), we are conducted to the following time discretization equation: begin{aligned} u^{k+1}=u^{k}+frac{Delta t}{2}left{ frac{partial ^2 (u^{k+1}{partialtial x^2}+frac{partial ^2 (u^{k})^2}{partial x^2}+frac{partial ^2 (u^{k+1}{partialtial y^2}+frac{partial ^2 (u^{k})^2}{partial y^2}+sigma [u^{k+1}]+sigma [u^k]right}.
Similar(59)
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