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m WP:CHECKWIKI error fix for #03. Missing Reflist. Do general fixes if a problem exists. - using AWB |
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The conservative form of Lax-Wendroff for a general non-linear equation is then
: <math> u_i^{n+1} = u_i^n - \frac{\Delta t}{2\Delta x} \left[ f(u_{i+1}^{n})) - f(u_{i-1}^{n}) \right] + \frac{\Delta t^2}{2\Delta x^2} \left[ A_{i+1/2}\left(f(u_{i+1}^{n}) - f(u_{i}^{n})\right) - A_{i-1/2}\left( f(u_{i}^{n})-f(u_{i-1}^{n})\right) \right].</math>
where <math>A_{i\pm 1/2}</math> is the Jacobian matrix evaluated at <math>\frac{1}{2}(U^n_i + U^n_{i\pm 1/2})</math>.
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