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- W2049672762 abstract "We establish rigorously convergence of a semi-discrete upwind scheme for the nonlinear variational wave equation $u_{tt} - c(u)(c(u) u_x)_x = 0$ with $u|_{t=0}=u_0$ and $u_t|_{t=0}=v_0$. Introducing Riemann invariants $R=u_t+c u_x$ and $S=u_t-c u_x$, the variational wave equation is equivalent to $R_t-c R_x=tilde c (R^2-S^2)$ and $S_t+c S_x=-tilde c (R^2-S^2)$ with $tilde c=c'/(4c)$. An upwind scheme is defined for this system. We assume that the the speed $c$ is positive, increasing and both $c$ and its derivative are bounded away from zero and that $R|_{t=0}, S|_{t=0}in L^1cap L^3$ are nonpositive. The numerical scheme is illustrated on several examples." @default.
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- W2049672762 date "2007-08-28" @default.
- W2049672762 modified "2023-09-27" @default.
- W2049672762 title "A convergent finite difference method for a nonlinear variational wave equation" @default.
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