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Currently displaying 1 – 2 of 2

Order by Relevance | Title | Year of publication

Implicit for local effects and explicit for nonlocal effects is unconditionally stable.

Anitescu, Mihai; Pahlevani, Faranak; Layton, William J. — 2004

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

An energy analysis of degenerate hyperbolic partial differential equations.

William J. Layton — 1984

Aplikace matematiky

An energy analysis is carried out for the usual semidiscrete Galerkin method for the semilinear equation in the region $Ω$ (E) ${(t u_{t})}_{t} = \sum_{i, j = 1} {(a_{i j} (x) u_{x_{i}})}_{x_{j}} - a_{0} (x) u + f (u)$ , subject to the initial and boundary conditions, $u = 0$ on $\partial Ω$ and $u (x, 0) = u_{0}$ . (E) is degenerate at $t = 0$ and thus, even in the case $f \equiv 0$ , time derivatives of $u$ will blow up as $t \to 0$ . Also, in the case where $f$ is locally Lipschitz, solutions of (E) can blow up for $t > 0$ in finite time. Stability and convergence of the scheme in $W^{2, 1}$ is shown in the linear case without assuming $u_{t t}$ (which can blow up as $t \to 0$ is...

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