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HWENO-FVM solves why the accuracy of u_t + u_x = 0 has always been around 1
% u_t + f(u)_x =0 u(x,0) = 0.5+sin(pi*x) % v_t + g(u,v)_x =0 v(x,0) = pi*cos(pi*x) % f(u) = u ,g(u,v) = ...

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