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 blow-up time when the mesh size goes to zero. Numerical experiments are analyzed.
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Jovanovic, B.S., Koleva, M.N., Vulkov, L.G. (2007). Numerical Analysis of Blow-Up Weak Solutions to Semilinear Hyperbolic Equations. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_73
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DOI: https://doi.org/10.1007/978-3-540-70942-8_73
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
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