A sixth order accurate AGE iterative method for non-linear singular two point boundary value problems

Article type: Research Article

Authors: Mohanty, R.K.^{a; *} | Evans, D.J.^b | Jha, Navnit^a

Affiliations: [a] Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi – 110 007, India | [b] Department of Computing, The Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, United Kingdom

Correspondence: [*] Corresponding author. E-mail: rmohanty@maths.du.ac.in.

Abstract: We report alternating group explicit (AGE) iteration method to solve the tri-diagonal linear system derived from a new finite difference discretization of sixth order accuracy of the two point singular boundary value problem u″+αru′=f(r), 0<r<1, α=1 and 2 subject to boundary conditions u(0)=A, u(1)=B, where A and B are finite constants. We also discuss Newton-AGE iteration method for the sixth order numerical solution of two point non-linear boundary value problem. The proof for the convergence of the AGE iteration method when the coefficient matrix is real and unsymmetric is discussed. Numerical results are presented to illustrate the proposed iterative methods.

Keywords: Sixth order method, AGE method, real unsymmetric coefficient matrix, Newton-AGE method, non-linear equation, singular equation, Burgers' equation

DOI: 10.3233/JCM-2006-61-406

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 6, no. 1-4, pp. 57-69, 2006