Abstract
In the paper an interval method for solving the one-dimensio-nal heat conduction equation with mixed boundary conditions is considered. The idea of the interval method is based on the finite difference scheme of the conventional Crank-Nicolson method adapted to the mixed boundary conditions. The interval method given in the form presented in the paper includes the error term of the conventional method.
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References
Jankowska, M.A., Marciniak, A.: An Interval Finite Difference Method for Solving the One-Dimensional Heat Equation. LNCS (accepted)
Lapidus, L., Pinder, G.F.: Numerical Solution of Partial Differential Equations in Science and Engineering. J. Wiley & Sons (1982)
Manikonda, S., Berz, M., Makino, K.: High-order verified solutions of the 3D Laplace equation. WSEAS Transactions on Computers 4(11), 1604–1610 (2005)
Marciniak, A.: An Interval Difference Method for Solving the Poisson Equation - the First Approach. Pro Dialog 24, 49–61 (2008)
Marciniak, A.: An Interval Version of the Crank-Nicolson Method – The First Approach. In: Jónasson, K. (ed.) PARA 2010, Part II. LNCS, vol. 7134, pp. 120–126. Springer, Heidelberg (2012)
Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. SIAM, Philadelphia (2009)
Nagatou, K., Hashimoto, K., Nakao, M.T.: Numerical verification of stationary solutions for Navier-Stokes problems. Journal of Computational and Applied Mathematics 199(2), 445–451 (2007)
Nakao, M.T.: Numerical verification methods for solutions of ordinary and partial differential equations. Numerical Functional Analysis and Optimization 22(3-4), 321–356 (2001)
Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods. Oxford University Press (1995)
Watanabe, Y., Yamamoto, N., Nakao, M.T.: A Numerical Verification Method of Solutions for the Navier-Stokes Equations. Reliable Computing 5(3), 347–357 (1999)
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Jankowska, M.A. (2012). An Interval Finite Difference Method of Crank-Nicolson Type for Solving the One-Dimensional Heat Conduction Equation with Mixed Boundary Conditions. In: Jónasson, K. (eds) Applied Parallel and Scientific Computing. PARA 2010. Lecture Notes in Computer Science, vol 7134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28145-7_16
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DOI: https://doi.org/10.1007/978-3-642-28145-7_16
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