Interval Versions of Central-Difference Method for Solving the Poisson Equation in Proper and Directed Interval Arithmetic

[1] Delphi Pascal IntervalArithmetic Unit, http://www.cs.put.poznan.pl/amarciniak/DEL-wyklady/IntervalArithmetic.pasSearch in Google Scholar

[2] Hammer, R., Hocks, M., Kulisch, U., Ratz, D.: Numerical Toolbox for Verified Computing I: Basic Numerical Problems, Springer, Berlin (1993)Search in Google Scholar

[3] Hoffmann, T., Marciniak, A.: Solving the Poisson Equation by an Interval Difference Method of the Second Order, Computational Methods in Science and Technology 19 (1), 13{21, (2013)Search in Google Scholar

[4] Marciniak, A.: An Interval Difference Method for Solving the Poisson Equation{ the First Approach, Pro Dialog 24, 49-61, (2008)Search in Google Scholar

[5] Marciniak, A.: Selected Interval Methods for Solving the Initial Value Problem, Publishing House of Poznan University of Technology, Poznan (2009)Search in Google Scholar

[6] Marciniak, A.: On Realization of Floating-Point Directed Interval Arithmetic, 2012, http://www.cs.put.poznan.pl/amarciniak/KONF-referaty/DirectedArithmetic.pdfSearch in Google Scholar

[7] Markov, S.: On Directed Interval Arithmetic and its Applications, Journal of Universal Computer Science 7, 514-526, (1995)Search in Google Scholar

[8] Nakao, M.T.: A Numerical Approach to the Pro_ of Existence of Solutions for Elliptic Problems, Japan Journal of Industrial and Applied Mathematics 5 (2), 313-332, (1988)Search in Google Scholar

[9] Nakao, M.T.: Numerical Verification Methods for Solutions of Ordinary and Partial Differential Equations, Numerical Functional Analysis and Optimization 22, 321-356, (2001)Search in Google Scholar

[10] Nakao, M.T., Watanabe, Y.: An E_cient Approach to the Numerical Verification for Solutions of Elliptic Differential Equations, Numerical Algorithms 37, 311-323, (2004)Search in Google Scholar

[11] Popova, E.D.: Extended Interval Arithmetic in IEEE Floating-Point Environ- ment, Interval Computations 4, 100-129, (1994)Search in Google Scholar

[12] Schwandt, H.: An Interval Arithmetic Approach for the Construction of an Al- most Globally Convergent Method for the Solution of Nonlinear Poisson Equation on the Unit Square, SIAM Journal of Scientific and Statistical Computing 5 (2), 427-452, (1984)Search in Google Scholar

[13] Schwandt, H.: Almost Globally Convergent Interval Methods for Discretizations of Nonlinear Elliptic Partial Differential Equations, SIAM Journal on Numerical Analysis 23 (2), 304-324, (1986)Search in Google Scholar

[14] Schwandt, H.: The Solution of Nonlinear Elliptic Dirichlet Problems on Rectan- gles by Almost Globally Convergent Interval Methods, SIAM Journal on Scientific and Statistical Computing 6 (3), 617-638, (1985) Search in Google Scholar