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ISRN Mathematical Physics

Volume 2012 (2012), Article ID 234516, 11 pages

http://dx.doi.org/10.5402/2012/234516

Research Article

## Cubic Spline Iterative Method for Poisson’s Equation in Cylindrical Polar Coordinates

^{1}Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110 007, India^{2}Department of Mathematics, Deenbandhu Chhotu Ram University of Science & Technology, Murthal 131039, India

Received 4 October 2011; Accepted 16 November 2011

Academic Editors: J.-C. Wallet and H. Zhou

Copyright © 2012 R. K. Mohanty et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Linked References

- R. E. Lynch and J. R. Rice, “High accuracy finite difference approximation to solutions of elliptic partial differential equations,”
*Proceedings of the National Academy of Sciences of the United States of America*, vol. 75, no. 6, pp. 2541–2544, 1978. View at Scopus - R. F. Boisvert, “Families of High order Accurate discretization of some elliptic problems,”
*SIAM Journal on Scientific Computing*, vol. 2, pp. 268–285, 1981. - I. Yavneh, “Analysis of a fourth-order compact scheme for convection-diffusion,”
*Journal of Computational Physics*, vol. 133, no. 2, pp. 361–364, 1997. View at Scopus - M.K. Jain, R.K. Jain, and R.K. Mohanty, “A fourth order difference method for elliptic equations with Non Linear first derivative terms,”
*Numerical Methods for Partial Differential Equations*, vol. 5, no. 2, pp. 87–95, 1989. - M. K. Jain, R. K. Jain, and R. K. Mohanty, “Fourth order difference methods for the system of 2-D nonlinear elliptic partial differential equations,”
*Numerical Methods for Partial Differential Equations*, vol. 7, pp. 227–244, 1991. - R. K. Mohanty, “Order
*h*^{4}difference methods for a class of singular two space elliptic boundary value problems,”*Journal of Computational and Applied Mathematics*, vol. 81, no. 2, pp. 229–247, 1997. View at Scopus - R. K. Mohanty and S. Dey, “A new finite difference discretization of order four for (
*∂*u/*∂*n) for two-dimensional quasi-linear elliptic boundary value problem,”*International Journal of Computer Mathematics*, vol. 76, no. 4, pp. 505–516, 2001. View at Scopus - R. K. Mohanty, S. Karaa, and U. Arora, “Fourth order nine point unequal mesh discretization for the solution of 2D nonlinear elliptic partial differential equations,”
*Neural, Parallel and Scientific Computations*, vol. 14, no. 4, pp. 453–470, 2006. View at Scopus - R. K. Mohanty and S. Singh, “A new fourth order discretization for singularly perturbed two dimensional non-linear elliptic boundary value problems,”
*Applied Mathematics and Computation*, vol. 175, no. 2, pp. 1400–1414, 2006. View at Publisher · View at Google Scholar · View at Scopus - W. G. Bickley, “Piecewise cubic interpolation and two-point boundary problems,”
*Computer Journal*, vol. 11, no. 2, pp. 206–208, 1968. View at Publisher · View at Google Scholar · View at Scopus - D. J. Fyfe, “The use of cubic splines in the solution of two point boundary value problems,”
*The Computer Journal*, vol. 12, pp. 188–192, 1969. - R. P. Tewarson, “On the use of splines for the numerical solution of nonlinear two-point boundary value problems,”
*BIT*, vol. 20, no. 2, pp. 223–232, 1980. View at Publisher · View at Google Scholar · View at Scopus - M. K. Jain and T. Aziz, “Cubic spline solution of two-point boundary value problems with significant first derivatives,”
*Computer Methods in Applied Mechanics and Engineering*, vol. 39, no. 1, pp. 83–91, 1983. View at Scopus - E. A. Al-Said, “Spline methods for solving system of second-order boundary-value problems,”
*International Journal of Computer Mathematics*, vol. 70, no. 4, pp. 717–727, 1999. View at Scopus - E. A. Al-Said, “The use of cubic splines in the numerical solution of a system of second-order boundary value problems,”
*Computers and Mathematics with Applications*, vol. 42, no. 6-7, pp. 861–869, 2001. View at Publisher · View at Google Scholar · View at Scopus - A. Khan, “Parametric cubic spline solution of two point boundary value problems,”
*Applied Mathematics and Computation*, vol. 154, no. 1, pp. 175–182, 2004. View at Publisher · View at Google Scholar · View at Scopus - R. K. Mohanty and D. J. Evans, “A fourth order accurate cubic spline alternating group explicit method for non-linear singular two point boundary value problems,”
*International Journal of Computer Mathematics*, vol. 80, no. 4, pp. 479–492, 2003. View at Publisher · View at Google Scholar · View at Scopus - R. K. Mohanty, P. L. Sachdev, and N. Jha, “An O(
*h*^{4}) accurate cubic spline TAGE method for nonlinear singular two point boundary value problems,”*Applied Mathematics and Computation*, vol. 158, no. 3, pp. 853–868, 2004. View at Publisher · View at Google Scholar · View at Scopus - J. Rashidinia, R. Mohammadi, and R. Jalilian, “Cubic spline method for two-point boundary value problems,”
*International Journal of Engineering Science*, vol. 19, pp. 39–43, 2008. - R. K. Mohanty and V. Dahiya, “An $O({k}^{2}+k{h}^{2}+{h}^{4})$ accurate two-level implicit cubic spline method for one space dimensional quasi-linear parabolic equations,”
*American Journal of Computational Mathematics*, vol. 1, no. 1, pp. 11–17, 2011. - R.K. Mohanty, R. Kumar, and V. Dahiya, “Cubic spline method for 1D wave equation in polar coordinates,”
*ISRN Computational Mathematics*, vol. 2012, Article ID 302923, 6 pages, 2012. View at Publisher · View at Google Scholar - R.S. Varga,
*Matrix Iterative Analysis*, Springer, New York, NY, USA, 2000. - Y. Saad,
*Iterative methods for Sparse Linear Systems*, SIAM, Philadelphia, Pa, USA, 2nd edition, 2003. - L. A. Hageman and D. M. Young,
*Applied Iterative Methods*, Dover, New York, NY, USA, 2004.