$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\tp}{\thinspace .} \newcommand{\Oof}[1]{\mathcal{O}(#1)} $$

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A centered finite difference scheme; step 4

Step 4: Formulate the computational algorithm. Assume \( u^{n-1} \) and \( u^n \) are known, solve for unknown \( u^{n+1} \): $$ u^{n+1} = 2u^n - u^{n-1} - \Delta t^2\omega^2 u^n $$

Nick names for this scheme: Stormer's method or Verlet integration.

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