bvpsuite

The New MATLAB 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


References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Gerdts, Matthias: A survey on optimal control problems with differential-algebraic equations (2015)
  2. Auzinger, Winfried; Koch, Othmar; Bagherzadeh, Amir Saboor: Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations (2014)
  3. Burkotová, Jana; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa B.: On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity (2014)
  4. Gschwindl, Jürgen; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa B.: Positive blow-up solutions of nonlinear models from real world dynamics (2014)
  5. Kulikov, G.Yu.; Lima, P.M.; Morgado, M.L.: Analysis and numerical approximation of singular boundary value problems with the $p$-Laplacian in fluid mechanics (2014)
  6. Dick, Alexander; Koch, Othmar; März, Roswitha; Weinmüller, Ewa: Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point (2013)
  7. Hastermann, G.; Lima, P.M.; Morgado, M.L.; Weinmüller, E.B.: Density profile equation with $p$-Laplacian: analysis and numerical simulation (2013)
  8. Rachůnková, Irena; Spielauer, Alexander; Staněk, Svatoslav; Weinmüller, Ewa B.: Positive solutions of nonlinear Dirichlet BVPs in ODEs with time and space singularities (2013)
  9. Rachůnková, Irena; Spielauer, Alexander; Staněk, Svatoslav; Weinmüller, Ewa B.: The structure of a set of positive solutions to Dirichlet BVPs with time and space singularities (2013)
  10. Feichtinger, Anna; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa: Periodic BVPs in ODEs with time singularities (2011)
  11. Hammerling, Robert; Koch, Othmar; Simon, Christa; Weinmüller, Ewa B.: Numerical solution of singular ODE eigenvalue problems in electronic structure computations (2010)
  12. Cash, J.; Kitzhofer, G.; Koch, O.; Moore, G.; Weinmüller, E.: Numerical solution of singular two point BVPs (2009)
  13. Kitzhofer, G.; Koch, O.; Weinmüller, E.: Numerical treatment of singular BVPs: the new Matlab code bvpsuite (2009)
  14. Staněk, Svatoslav; Pulverer, Gernot; Weinmüller, Ewa B.: Analysis and numerical simulation of positive and dead-core solutions of singular two-point boundary value problems (2008)