Pandey, R. K.; Singh, Arvind K. A new high-accuracy difference method for a class of weakly nonlinear singular boundary-value problems. (English) Zbl 1114.65091 Int. J. Comput. Math. 83, No. 11, 809-817 (2006). Summary: A fourth-order finite difference method based on a uniform mesh is described by using Chawla’s identity [cf. M. Sakai and R. A. Usmani, BIT 30, No. 3, 566–568 (1990; Zbl 0705.65059)] for a class of singular two point boundary-value problems \[ (p(x)y')'=p(x)f(x,y),\;0<x\leq 1;\;y(0)=A,\;\alpha y(1)+\beta y'(1)=\gamma \] with \(p(x)>0\) on \((0,1]\) and \(p(x)=x^{b_0}g(x)\), for all \(x\) in \((0,1]\), \(0\leq b_0< 1\). Fourth-order convergence is established under quite general conditions on \(f(x,y)\). The method reduces to Numerov’s method for \(p(x)=1\) and boundary conditions \(y(0)=A\), \(y(1)=B\). This method provides better results than some existing fourth-order methods ford \(p(x)=x^{b_0}\), \(0\leq b_0<1\) and boundary conditions \(y(0)=A\), \(y(1)=B\), which is verified by two examples and also the order of the method is verified for general functions \(p(x)\). Cited in 4 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65L12 Finite difference and finite volume methods for ordinary differential equations 34B16 Singular nonlinear boundary value problems for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations Keywords:numerical example; singular two point boundary-value problems; convergence; Numerov’s method Citations:Zbl 0705.65059 PDFBibTeX XMLCite \textit{R. K. Pandey} and \textit{A. K. Singh}, Int. J. Comput. Math. 83, No. 11, 809--817 (2006; Zbl 1114.65091) Full Text: DOI References: [1] DOI: 10.1007/BF01407867 · Zbl 0489.65055 · doi:10.1007/BF01407867 [2] DOI: 10.1016/0377-0427(87)90112-9 · Zbl 0614.65087 · doi:10.1016/0377-0427(87)90112-9 [3] DOI: 10.1016/0377-0427(88)90267-1 · Zbl 0634.65064 · doi:10.1016/0377-0427(88)90267-1 [4] DOI: 10.1007/BF02165374 · Zbl 0211.19103 · doi:10.1007/BF02165374 [5] DOI: 10.1007/BF01436387 · Zbl 0255.65032 · doi:10.1007/BF01436387 [6] DOI: 10.1007/BF02165591 · Zbl 0179.22103 · doi:10.1007/BF02165591 [7] DOI: 10.1016/j.cam.2003.09.053 · Zbl 1086.65083 · doi:10.1016/j.cam.2003.09.053 [8] DOI: 10.1007/BF01954906 · Zbl 0665.65067 · doi:10.1007/BF01954906 [9] DOI: 10.1007/BF01931669 · Zbl 0705.65059 · doi:10.1007/BF01931669 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.