Abstract
The proposed in [7] uniform error estimate allows to control the accuracy of the symbolic approximate solution of the Dirichlet problem for elliptic PDE in the whole domain of the problem considered. The present paper demonstrates the techniques of finding such an approximate solution with Mathematica and the use of the uniform error estimate for a concrete example.
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References
Wolfram, S.: The Mathematica Book, 4th edn. Wolfram Media, Champain (1999)
Dzyadyk, V.K.: Approximated methods for solving differential and integral equations. Nauk. dumka, Kiev (1988)
Hantzschmann, K.: Zur Lösung von Randwertaufgaben bei Systemen gewönlichen Deifferentialgleichungen mit dem Ritz-Galerkin-Verfahren. Habilitationsschrift Technische Universitet Dresden (1983)
Lehmann, N.J.: Fehlerschranken für Näherungslösungen bei Differentialgleichungen. Numerische Mathematik 10, 261–288 (1967)
Becken, O., Jung, A.: Error estimation in the case of linear ordinary differential equations. Rostoker Informatik-Berichte 22 (1998)
Rösler, T.: Adaptiv-iteratives Verfahren zur Lsung von Differenzialgleichungen. Rostoker Informatik-Berichte 28, 89–108 (2003)
Zemskov, S.: The Error Estimate of the Approximate Solution of the Dirichlet Problem for Elliptical Partial Differential Equation. Computer Algebra in Scientific Computing. In: Proceedings of the Seventh International Workshop, pp. 479–484. Technische Universität München (2004)
Mihajlov, V.P.: Partial differential equations. Nauka, Moskva, (1976) (in Russian)
Polianin, A.D.: Handbook of Linear Partial Differential Equations for Engineers and Scientists. Chapman & Hill/CRC, Boca Raton (2002)
Koshliakov, N.S., Gliner, E.B., Smirnov, M.M.: Differential equations of mathematical physics. Moskva, State Publishing House for physical and mathematical literature (1962) (in Russian)
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Zemskov, S. (2005). Approximate Solution of the Dirichlet Problem for Elliptic PDE and Its Error Estimate. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_41
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DOI: https://doi.org/10.1007/11555964_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28966-1
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