Journal ArticleDOI
On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems
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In this paper, the authors consider a linear ordinary differential equation of the 2nd order which has a singularity at the origin, and according to the nature of this singularity, they must consider either the two-point boundary-value problem or the onepoint boundary value problem.Abstract:
Consider a linear ordinary differential equation of the 2nd order which has a singularity at the origin; according to the nature of this singularity we must consider either the two-point boundary-value problem or the one-point boundary value problem. Finite-difference schemes are studied; results are given concerning error analysis and monotone convergence.read more
Citations
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Book ChapterDOI
Use of Green's functions in the numerical solution of two-point boundary value problems
L. J. Gallaher,I. E. Perlin +1 more
TL;DR: In this article, the authors investigated the use of Green's functions in the numerical solution of the two-point boundary value problem and provided procedures for numerical construction of such functions and conditions for their existence.
Journal ArticleDOI
Stability of singular boundary value problems and their discretization by finite differences
TL;DR: In this article, the stability bounds for the solution of nonlinear singular boundary value problem for systems of ordinary differential equations of second order were derived, where the stability of a finite difference method is related to the stability in the analytical problem being solved.
Journal ArticleDOI
Numerical solution of singular regular boundary value problems by pole detection with qd-algorithm
H. Allouche,N. Marhraoui +1 more
TL;DR: This paper presents a method using qd-algorithm combined with finite difference method for numerically solving singular boundary value problems for certain ordinary differential equation having singular coefficients.
Journal ArticleDOI
Optimal Mortgage Prepayment Under the Cox--Ingersoll--Ross Model
Chris Jones,Xinfu Chen +1 more
TL;DR: An analysis of the economic incentive to prepay a mortgage depends on the yield curve of interest rates under the assumption that the term structure is defined by the Cox--Ingersoll--Ross (CIR) model for the short rate.
Use of Green's functions in the numerical solution of two-point boundary value problems Final report, 1 Apr. 1970 - 31 Mar. 1971
L. J. Gallaher,I. E. Perlin +1 more
TL;DR: Green function in solving linear and nonlinear second order ordinary differential equations including examples in finding rendezvous and periodic orbits of restricted three body systems is used in this paper, where it is shown to be useful in finding periodic orbits and rendezvous.
References
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Journal ArticleDOI
Numerical Methods for Generalized Axially Symmetric Potentials
TL;DR: A generalized axially symmetric potential (GASP) in n = k + 2 "dimensions" has been studied in this article, where the GASP is defined as a harmonic function in ndimensions having certain symmetry properties.
Journal ArticleDOI
Numerical Methods for Elliptic Differential Equations Whose Coefficients are Singular on a Portion of the Boundary
Pierre Jamet,Seymour V. Parter +1 more
Journal ArticleDOI
Numerical methods and existence theorems for parabolic differential equations whose coefficients are singular on the boundary
TL;DR: In this paper, the authors studied finite-difference methods for elliptic differential equations of the second order whose coefficients are singular on a portion of the boundary; the uniform convergence of the approximations and the existence of a solution of the Dirichlet problem were proved for a class of such equations.
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