Finite difference methods and their convergence for a class of singular two point boundary value problems |
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Authors: | M M Chawla C P Katti |
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Institution: | (1) Department of Mathematical Sciences, New Mexico State University, 88003 Las Cruces, New Mexico, USA;(2) Department of Mathematics, Indian Institute of Technology, Hauz Khas, 110016 New Delhi, India |
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Abstract: | Summary We discuss the construction of three-point finite difference approximations and their convergence for the class of singular two-point boundary value problems: (x
y)=f(x,y), y(0)=A, y(1)=B, 0<<1. We first establish a certain identity, based on general (non-uniform) mesh, from which various methods can be derived. To obtain a method having order two for all (0,1), we investigate three possibilities. By employing an appropriate non-uniform mesh over 0,1], we obtain a methodM
1 based on just one evaluation off. For uniform mesh we obtain two methodsM
2 andM
3 each based on three evaluations off. For =0,M
1 andM
2 both reduce to the classical second-order method based on one evaluation off. These three methods are investigated, theirO(h
2)-convergence established and illustrated by numerical examples. |
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Keywords: | AMS(MOS): 65L10 CR: 5 17 |
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