Skip to main content
Log in

Numerical diagnosis of blow-up of solutions of pseudoparabolic equations

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. N. N. Kalitkin, “Numerical methods for solving sti. systems,” Mat. Modelirovanie, 7, No. 5, 8–11 (1995).

    MATH  Google Scholar 

  2. E. Hairer and G. Wanner, Solving of Ordinary Differential Equations. Stiff and Differential-Algebraic Problems [Russian translation], Mir, Moscow (1999).

    Google Scholar 

  3. H. H. Rosenbrock, “Some general implicit processes for the numerical solution of differential equations,” Comput. J., 5, No. 4, 329–330 (1963).

    Article  MATH  MathSciNet  Google Scholar 

  4. G. I. Marchuk and V. V. Shaidurov, Increase in Accuracy of Solutions to Difference Schemes [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  5. 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).

    Google Scholar 

  6. 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).

    Google Scholar 

  7. 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).

    MathSciNet  Google Scholar 

  8. 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).

  9. 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).

  10. 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).

  11. 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).

    MATH  MathSciNet  Google Scholar 

  12. 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).

    MathSciNet  Google Scholar 

  13. 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).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. A. Al’shina.

Additional information

__________

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 40, Differential Equations, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-007-0542-2

Keywords

Navigation