Hindawi Publishing Corporation Advances in Numerical Analysis Volume 2013, Article ID 614508, 10 pages http://dx.doi.org/10.1155/2013/614508
Research Article Geometric Mesh Three-Point Discretization for Fourth-Order Nonlinear Singular Differential Equations in Polar System Navnit Jha,1 R. K. Mohanty,1,2 and Vinod Chauhan2 1 2
Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi 110021, India Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India
Correspondence should be addressed to Navnit Jha;
[email protected] Received 9 June 2013; Revised 8 August 2013; Accepted 23 August 2013 Academic Editor: R¨udiger Weiner Copyright © 2013 Navnit Jha 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. Numerical method based on three geometric stencils has been proposed for the numerical solution of nonlinear singular fourthorder ordinary differential equations. The method can be easily extended to the sixth-order differential equations. Convergence analysis proves the third-order convergence of the proposed scheme. The resulting difference equations lead to block tridiagonal matrices and can be easily solved using block Gauss-Seidel algorithm. The computational results are provided to justify the usefulness and reliability of the proposed method.
1. Introduction Consider the fourth-order boundary value problem: 𝑢(4) (𝑟) = 𝑓 (𝑟, 𝑢 (𝑟) , 𝑢(1) (𝑟) , 𝑢(2) (𝑟) , 𝑢(3) (𝑟)) , 𝛼
