The New MATLAB Code bvpsuite for the Solution of Singular Implicit BVPs1

G. Kitzhofer, O. Koch, G. Pulverer, Ch. Simon, and E.B. Weinmï¿œuller2
Institute for Analysis and Scientific Computing (E101),
Vienna University of Technology,
Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria
Received 21 January, 2010; accepted in revised form 23 March, 2010
Abstract: Our aim is to provide the open domain MATLAB code bvpsuite for the efficient numerical
solution of boundary value problems in ordinary differential equations. Motivated by applications,
we are especially interested in designing a code whose scope is appropriately wide, including fully implicit
problems of mixed orders, parameter dependent problems, problems with unknown parameters,
problems posed on semi-infinite intervals, eigenvalue problems and differential algebraic equations
of index 1. Our main focus is on singular boundary value problems in which singularities in the differential
operator arise. We first briefly recapitulate the analytical properties of singular systems and
the convergence behavior of polynomial collocation used as a basic solver in the code for both singular
and regular ordinary differential equations and differential algebraic equations. We also discuss
the a posteriori error estimate and the grid adaptation strategy implemented in our code. Finally, we
describe the code structure and present the performance of the code which has been equipped with a
graphical user interface for an easy use.

 

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