Communications in Mathematical Sciences

Automatic coordinate transformation for two-point boundary value problems

Aaditya V. Rangan

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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.

Article information

Commun. Math. Sci., Volume 5, Issue 3 (2007), 723-741.

First available in Project Euclid: 29 August 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65N99: None of the above, but in this section

linear two-point boundary value problems spectral integral methods boundary matrices


Rangan, Aaditya V. Automatic coordinate transformation for two-point boundary value problems. Commun. Math. Sci. 5 (2007), no. 3, 723--741.

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