## Communications in Mathematical Sciences

### Automatic coordinate transformation for two-point boundary value problems

#### Abstract

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

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

Dates
First available in Project Euclid: 29 August 2007

https://projecteuclid.org/euclid.cms/1188405676

Mathematical Reviews number (MathSciNet)
MR2352339

Zentralblatt MATH identifier
1133.65053

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

#### Citation

Rangan, Aaditya V. Automatic coordinate transformation for two-point boundary value problems. Commun. Math. Sci. 5 (2007), no. 3, 723--741. https://projecteuclid.org/euclid.cms/1188405676