Journal ArticleDOI
Numerical Methods for Singular Boundary Value Problems
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In this article, the authors treat some nonlinear two-point boundary value problems for certain ordinary differential equations having singular coefficients and compare traditional finite differences, patch bases and collocation as computational methods.Abstract:
The authors treat some nonlinear two-point boundary value problems for certain ordinary differential equations having singular coefficients. Typically these problems arise when reducing partial to ordinary differential equations by physical symmetry. Traditional finite differences, patch bases and collocation are all developed and compared as computational methods.read more
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Journal ArticleDOI
A collocation solver for mixed order systems of boundary value problems
TL;DR: Implementation of a spline collocation method for solving boundary value problems for mixed order systems of ordinary differential equations is discussed and the resulting general purpose code, COLSYS, is tested on a number of examples to demonstrate its stability, efficiency and flexibility.
Journal ArticleDOI
A method for the spatial discretization of parabolic equations in one space variable
Robert D. Skeel,Martin Berzins +1 more
TL;DR: In this article, a spatial discretization method for polar and nonpolar parabolic equations in one space variable is proposed, which is suitable for use in a library program.
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A new method for solving singular initial value problems in the second-order ordinary differential equations
TL;DR: Singular initial value problems, linear and nonlinear, homogeneous and nonhomogeneous, are investigated by using Adomian decomposition method and a new general formula is established.
Journal ArticleDOI
Legendre wavelets method for solving differential equations of Lane-Emden type
TL;DR: The properties of Legendre wavelet are first presented and these properties together with the Gaussian integration method are utilized to reduce the integral equations to the solution of algebraic equations.
Journal ArticleDOI
Difference Methods for Boundary Value Problems with a Singularity of the First Kind
Frank de Hoog,Richard Weiss +1 more
TL;DR: In this paper, the application of different difference schemes (box, trapezoidal, Euler and backward Euler) to numerical solution of boundary value problems for nonlinear first order systems of ordinary differential equations with a singularity of the first kind is examined.