329 Asian J. Exp. Sci., Vol. 23, No. 1, 2009; 329-340 Design and Analysis of Quarter Sweep ADEI Algorithm for Linear and Nonlinear Two Point Boundary Value Problems Containing Singularity: Application to Burger's Equation Navnit Jha 1 *, Bhupendra K. Sharma 1 and R.C. Chaudhary 2 1 Mathematics Group, Birla Institute of Technology & Science, Pilani-333031 (Raj.); India. 2 Department of Mathematics, University of Rajasthan, Jaipur-302004 (Raj.); India. Abstract : The formulation of quarter sweep alternating decomposition explicit iterative (QSADEI) method for the numerical solution of the non linear singular equations is discussed in this paper. The concept of QSADEI method was inspired via combination between the quarter sweep iterative and alternating decomposition explicit iterative (ADEI) methods. The proposed QSADEI method shows the superiority over the corresponding Gauss seidal iterative method. The method is applicable to problems both in Cartesian and polar coordinates. The convergence analysis is briefly discussed. Numerical results are provided to illustrate the proposed method. Key words : Full-, Half-, Quarter-sweep methods, Alternating Decomposition explicit method, Fourth order method, Singular equations, Burger’s equations, RMS errors. Introduction Consider the non linear two point boundary value problem ( ) b t a u u t g u < < = + − , 0 , , ' ' ' ....... (1) subject to the natural boundary conditions ( ) A a u = , ( ) B b u = The two point boundary value problem mentioned above has a unique solution (Keller 1968) and is of common occurrence in many fields of science and engineering, e.g., geophysics, quantum mechanics, fluid dynamics, aerodynamics, etc. There are many methods available for the above problems. Quarter sweep alternating decomposition explicit iterative (QSADEI) method is one of them. The quarter sweep iterative method was initiated by Othman and Abdullah, 2000. The concept of this method is extension of half sweep iterative method through explicit decoupled group iterative method (Yousif and Evans, 1995). The QSADEI method explained in this paper is combination of quarter sweep iterative method and alternating decomposition explicit iterative (ADEI) method, earlier discussed by Sahimi et. al., 1993; Sulaiman et. al., 2004 has considered QSADEI method for solving one dimensional diffusion equations, where the theoretical convergence of the method is not discussed and their methods are only applicable to non singular problems. Difficulties were experienced in the past for the numerical solution of singular equations in polar coordinate. The solution usually deteriorates in the vicinity of singularity. In this paper, the method is refined in such a manner that solutions retain their order and accuracy everywhere in the solution region even in the vicinity of the singularity. We also discuss QSADEI and Newton- * Corresponding author : Navnit Jha, Mathematics Group, Birla Institute of Technology & Science, Pilani-333031 (Raj.); India; E-mail : navnitjha@hotmail.com