The New M ATLAB Code bvpsuite for the Solution of Singular Implicit BVPs

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. Keywords: Boundary value problems – singularity of the first kind – singularity of the second kind – analysis – collocation methods – a posteriori error estimation – mesh adaptation – pathfollowing – eigenvalue problems – index-1 differential algebraic equations