A Note on Fourth Order Method for Doubly Singular Boundary Value Problems. (5th December 2012)

• Record Type: Journal Article
• Authors: Pandey, R. K.; Gupta, G. K.
• Other Names: Safouhi Hassan Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2012(2012)
• Publication Date: 2012-12-05
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2012/349618
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : We present a fourth order finite difference method for doubly singular boundary value problem ( p ( x ) y ′ ( x ) ) ′ = q ( x ) f ( x, y ), 0 < x ≤ 1 with boundary conditions y ( 0 ) = A ( or y ' ( 0 ) = 0 or lim x → 0 p ( x ) y ' ( x ) = 0 ) and α y ( 1 ) + β y ' ( 1 ) = γ, where α ( > 0 ), β ( ≥ 0 ), γ and A are finite constants. Here p ( 0 ) = 0 and q ( x ) is allowed to be discontinuous at the singular point x = 0 . The method is based on uniform mesh. The accuracy of the method is established under quite general conditions and also corroborated through one numerical example.