Numerical Analysis of Blow-Up Weak Solutions to Semilinear Hyperbolic Equations
Published Aug 20, 2006 · B. Jovanovic, M. Koleva, L. Vulkov
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Abstract
We study numerical approximations of weak solutions of hyperbolic problems with discontinuous coefficients and nonlinear source terms in the equation. By a semidiscretization of a Dirichlet problem in the space variable we obtain a system of ordinary differential equations (SODEs), which is expected to be an approximation of the original problem. We show at conditions similar to those for the hyperbolic problem, that the solution of the SODEs blows up. Under certain assumptions, we also prove that the numerical blow-up time converges to the real blowup time when the mesh size goes to zero. Numerical experiments are analyzed.
Study Snapshot
Key takeawayThe solution of a system of ordinary differential equations (SODEs) blows up under certain conditions, and the numerical blow-up time converges to the real blowup time when the mesh size goes to zero.
PopulationOlder adults (50-71 years)
Sample size24
MethodsObservational
OutcomesBody Mass Index projections
ResultsSocial networks mitigate obesity in older groups.