References
N. N. Kalitkin, “Numerical methods for solving sti. systems,” Mat. Modelirovanie, 7, No. 5, 8–11 (1995).
E. Hairer and G. Wanner, Solving of Ordinary Differential Equations. Stiff and Differential-Algebraic Problems [Russian translation], Mir, Moscow (1999).
H. H. Rosenbrock, “Some general implicit processes for the numerical solution of differential equations,” Comput. J., 5, No. 4, 329–330 (1963).
G. I. Marchuk and V. V. Shaidurov, Increase in Accuracy of Solutions to Difference Schemes [in Russian], Nauka, Moscow (1979).
N. N. Kalitkin, A. B. Al’shin, E. A. Al’shina, and B. V. Rogov, Computations on Quasi-Uniform Grids [in Russian], Fizmatlit, Moscow (2005).
E. A. Al’shina, N. N. Kalitkin, and P. V. Koryakin, “Diagnosis of singularities of the exact solution in computations with accuracy control,” Dokl. Ross. Akad. Nauk, 72, No. 2, 607–701 (2005).
E. A. Al’shina, N. N. Kalitkin, and P. V. Koryakin, “The singularity diagnostic in calculations with accuracy control,” Computational Mathematics and Mathematical Physics, 45, No. 10, 1769–1779 (2005).
A. V. Al’shin, E. A. Alshina, N. N. Kalitkin, and A. B. Koryagina, “The numerical solution of super-stiff differential-algebraic systems,” Dokl. Math. (2006).
M. O. Korpusov and A. G. Sveshnikov, “On blow-up of solutions of semilinear equations of pseudoparabolic type with rapidly growing nonlinearities,” Zh. Vychisl. Mat. Mat. Fiz (2005) (in press).
M. O. Korpusov and A. G. Sveshnikov, “On blow-up of solutions of nonlinear wave equations of the Sobolev type with cubic sources,” Mat. Zametki (2005) (in press).
M. O. Korpusov and A. G. Sveshnikov, “Three-dimensional nonlinear evolutionary equations of pseudoparabolic type in problems of mathematical physics,” Zh. Vychisl. Mat. Mat. Fiz., 43, No. 12, 1835–1869 (2003).
M. O. Korpusov and A. G. Sveshnikov, “On blow-up of a strongly nonlinear equation of pseudoparabolic type with double nonlinearity,” Zh. Vychisl. Mat. Mat. Mat. Fiz., 43, No. 7, 944–962 (2003).
M. O. Korpusov and A. G. Sveshnikov, “On blow-up of a solution of an initial-boundary-value problem for a nonlinear, nonlocal equation of pseudoparabolic type,” Zh. Vychisl. Mat. Mat. Fiz., No. 12 (2004).
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 40, Differential Equations, 2006.
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Al’shin, A.B., Al’shina, E.A. Numerical diagnosis of blow-up of solutions of pseudoparabolic equations. J Math Sci 148, 143–162 (2008). https://doi.org/10.1007/s10958-007-0542-2
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DOI: https://doi.org/10.1007/s10958-007-0542-2