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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
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Analytical method and its convergence analysis based on homotopy analysis for the integral form of doubly singular boundary value problems
TL;DR: In this article, a new formulation of the singular boundary value problems is presented to overcome the singular behavior at the origin, with the help of Green's function theory, the problem is transformed into an equivalent Fredholm integral equation and the optimal homotopy analysis method is applied to solve integral form of problem.
Journal Article
Solving Two-Points Singular Boundary Value Problem Using Hermite Interpolation
TL;DR: In this paper, the authors have used the Hermite interpolation method to solve second order regular boundary value problems for singular ordinary differential equations, where the solution of the equation is equal to summation of the solution in each subdomain.
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Scandalously Parallelizable Mesh Generation
David M. Bortz,Andrew Christlieb +1 more
TL;DR: How the near-perfect paralellizability of the approach suggests that these strategies have the potential for highly efficient utilization of massively parallel multi-core technologies such as General Purpose Graphics Processing Units (GPGPU's) is discussed.
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.
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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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