Open Access
September 2007 Automatic coordinate transformation for two-point boundary value problems
Aaditya V. Rangan
Commun. Math. Sci. 5(3): 723-741 (September 2007).


When one is attempting to build a general boundary value problem solver which uses Green’s functions, it is often desirable to automatically transform inhomogeneous boundary value problems into homogeneous boundary value problems. If the sum of the boundary matrices is singular, a change of coordinates is required which can transform the inhomogeneous boundary value problem into a homogeneous boundary value problem. This change of coordinates is an invertible C1 path in matrix space with endpoints that can multiply the boundary matrices to produce a nonsingular sum. Here we propose a simple automatic coordinate transformation that performs this task. We prove that this algorithm constructs a coordinate transformation whenever such a transformation exists, and provide numerical examples illustrating the practicability of the method.


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Aaditya V. Rangan. "Automatic coordinate transformation for two-point boundary value problems." Commun. Math. Sci. 5 (3) 723 - 741, September 2007.


Published: September 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1133.65053
MathSciNet: MR2352339

Primary: 65N99

Keywords: boundary matrices , linear two-point boundary value problems , spectral integral methods

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 3 • September 2007
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