An interval difference method for solving the wave equation

• Autorzy: Szyszka B.
• Konferencja: Computer Applications in Electrical Engineering 2012 (23-24.04.2012; Poznań, Polska)
• Języki publikacji: EN

Abstrakty

EN

In the paper a difference interval method for solving the wave equation together the initial-boundary value problems is presented. Using an interval method together floating-point interval arithmetic guarantee, that obtained interval solutions contain all numerical errors. Additionally, each exact solution is included into interval solution. In numerical experiments it is guarantee contain all numerical errors in obtained interval solutions. Taken into consideration is the central discretization method with regard to space and time. An initial condition is approximated by the third-order Taylor polynomial with local truncation error of order 0(h4). In the paper new formula, which described discretization of the initial condition, is proposed. Therefore more exact solutions are obtained then in the previous considerations.

Słowa kluczowe

EN

wave equation; difference interval method; interval method; floating point interval arithmetic

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Poznan University of Technology Academic Journals. Electrical Engineering
• Rocznik: 2012
• Tom: No. 69
• Strony: 161--168
• Opis fizyczny: bibliogr. 10 poz., rys., tab.

Twórcy

autor

Szyszka B.

• Poznan University of Technology

Bibliografia

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• [4] Kącki E., Partial Differential Equations in physics and techniques problems, WNT Warszawa 1995 (in Polish).
• [5] Marciniak A., Szyszka B., An interval method for solving some partial differential equations of second order, Proceedings on CD: 80th Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2009.
• [6] Moore R.E., Methods and Applications of Interval Analysis, SIAM, 1979.
• [7] Szyszka B., An Interval Difference Method for Solving Hyperbolic Partial Differential Equations, Mathematical Methods and Techniques in Engineering and Environmental Science, MACMESE Conference, p. 330-334, WSEAS Press, 2011.
• [8] Szyszka, B., Central difference interval method for solving the wave equation. ICNAAM (International Conference on Numerical Analysis and Applied Mathematics) 2010. AIP Conference Proceedings, vol. 1281, pp. 2173-2176, 2010.
• [9] Szyszka B., The Central Difference Interval Method for Solving the Wave Equation, Lecture Notes in Computer Science, Springer-Verlag, Berlin, (in print).
• [10] Zill D.G., Differential Equations with Boundary-Value Problems, PWS Publishers, Boston, 1986.