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Numerical Analysis and Applications

2015 year, number 1

A new coupled reduced alternating group explicit method for non–linear singular two point boundary value problems on a variable mesh

R. K. Mohanty1, Jyoti Talwar2
1Department of Applied Mathematics Faculty of Mathematics and Computer Science South Asian University Akbar Bhawan, Chanakyapuri New Delhi, 110021, India
2Department of Mathematics Faculty of Mathematical Sciences University of Delhi, Delhi, 110 007, India
Keywords: two point singular boundary value problems, geometric mesh, third order method, singular equation, CRAGE method, Newton-CRAGE method, Burgers equation, RMS errors

Abstract

In this paper, we discuss a new coupled reduced alternating group explicit (CRAGE) and Newton-CRAGE iteration methods to solve non-linear singular two point boundary value problems u″ = ƒ(r,u,u′), 0< r<1, subject to given natural boundary conditions u(0) = A1, u(1) = A2, where A1 and A2 are finite constants, along with a third order numerical method on a geometric mesh. The proposed method is applicable to singular and non-singular problems. We discuss the convergence of the CRAGE iteration method in detail. The results obtained from the proposed CRAGE iteration method are compared with the results of the corresponding two parameter alternating group explicit (TAGE) iteration methods to demonstrate computationally the efficiency of the proposed method.