A TAGE iterative method for the solution of non-linear singular two point boundary value problems using a sixth order discretization

• Published in: Applied mathematics and computation Vol. 180; no. 2; pp. 538 - 548
• Main Authors: Mohanty, R.K., Arora, Urvashi
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.09.2006; Elsevier
• Subjects: Burgers’ equation; Exact sciences and technology; Mathematical analysis; Mathematics; Newton-TAGE method; Non-linear equation; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Ordinary differential equations; Partial differential equations; Real unsymmetric coefficient matrix; Sciences and techniques of general use; Singular equation; Sixth order method; TAGE method; Newton-TAGE method; Singular equation; Burgers’ equation; Non-linear equation; Sixth order method; TAGE method; Real unsymmetric coefficient matrix; Numerical linear algebra; Iterative method; Numerical method; Burgers equation; Partial differential equation; Convergence; Non linear equation; Direct method; Numerical analysis; Boundary value problem; Linear system; Matrix inversion; Applied mathematics; Two point boundary value problem; Numerical solution; Matrix method; Burgers' equation
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2005.12.038

We report two parameter alternating group explicit (TAGE) 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 ″ + α r u ′ = 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-TAGE iteration method for the sixth order numerical solution of two point non-linear boundary value problem. The proof for the convergence of the TAGE iteration method when the coefficient matrix is real and unsymmetric is discussed. Numerical results are presented to illustrate the proposed iterative methods.