On some finite difference schemes for solution of hyperbolic heat conduction problems

• Autorzy: Raimondas Čiegis , Aleksas Mirinavičius
• Języki publikacji: EN

Abstrakty

EN

We consider the accuracy of two finite difference schemes proposed recently in [Roy S., Vasudeva Murthy A.S., Kudenatti R.B., A numerical method for the hyperbolic-heat conduction equation based on multiple scale technique, Appl. Numer. Math., 2009, 59(6), 1419–1430], and [Mickens R.E., Jordan P.M., A positivity-preserving nonstandard finite difference scheme for the damped wave equation, Numer. Methods Partial Differential Equations, 2004, 20(5), 639–649] to solve an initial-boundary value problem for hyperbolic heat transfer equation. New stability and approximation error estimates are proved and it is noted that some statements given in the above papers should be modified and improved. Finally, two robust finite difference schemes are proposed, that can be used for both, the hyperbolic and parabolic heat transfer equations. Results of numerical experiments are presented.

Słowa kluczowe

EN

Hyperbolic heat conduction; Finite difference method; Stability analysis; Convergence analysis

Kategorie tematyczne

• 65M06: Finite difference methods
• 65M12: Stability and convergence of numerical methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 5
• Strony: 1164-1170

Daty

wydano

2011-10-01

online

2011-07-26

Twórcy

autor

Raimondas Čiegis

• Vilnius Gediminas Technical University

autor

Aleksas Mirinavičius

• Vilnius Gediminas Technical University

Bibliografia

• [1] Čiegis R., Numerical solution of hyperbolic heat conduction equation, Math. Model. Anal., 2009, 14(1), 11–24 http://dx.doi.org/10.3846/1392-6292.2009.14.11-24
• [2] Čiegis R., Dement’ev A., Jankevičiūtė G., Numerical analysis of the hyperbolic two-temperature model, Lith. Math. J., 2008, 48(1), 46–60 http://dx.doi.org/10.1007/s10986-008-0005-6
• [3] Kalis H., Buikis A., Method of lines and finite difference schemes with the exact spectrum for solution the hyperbolic heat conduction equation, Math. Model. Anal., 2011, 16(2), 220–232 http://dx.doi.org/10.3846/13926292.2011.578677
• [4] Manzari Meh.T., Manzari Maj.T., On numerical solution of hyperbolic heat conduction, Comm. Numer. Methods Engrg., 1999, 15(12), 853–866 http://dx.doi.org/10.1002/(SICI)1099-0887(199912)15:12<853::AID-CNM293>3.0.CO;2-V
• [5] Mickens R.E., Jordan P.M., A positivity-preserving nonstandard finite difference scheme for the damped wave equation, Numer. Methods Partial Differential Equations, 2004, 20(5), 639–649 http://dx.doi.org/10.1002/num.20003
• [6] Roy S., Vasudeva Murthy A.S., Kudenatti R.B., A numerical method for the hyperbolic-heat conduction equation based on multiple scale technique, Appl. Numer. Math., 2009, 59(6), 1419–1430 http://dx.doi.org/10.1016/j.apnum.2008.09.001
• [7] Samarskii A.A., The Theory of Difference Schemes, Monogr. Textbooks Pure Appl. Math., 240, Marcel Dekker, New York, 2001 http://dx.doi.org/10.1201/9780203908518
• [8] Samarskii A.A., Matus P.P., Vabishchevich P.N., Difference Schemes with Operator Factors, Math. Appl., 546, Kluwer, Dordrecht, 2002
• [9] Sarra S.A., Spectral methods with postprocessing for numerical hyperbolic heat transfer, Numerical Heat Transfer, Part A, 2003, 43(7), 717–730 http://dx.doi.org/10.1080/713838126
• [10] Shen W., Han S., A numerical solution of two-dimensional hyperbolic heat conduction with non-linear boundary conditions, Heat and Mass Transfer, 2003, 39(5–6), 499–507

Identyfikatory

DOI

10.2478/s11533-011-0056-5