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

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  1. Auer, Felix Karl; Auzinger, Winfried; Burkotová, Jana; Rachůnková, Irena; Weinmüller, Ewa B.: On nonlinear singular BVPs with nonsmooth data. II: Convergence of collocation methods (2022)
  2. Fu, Guanxing; Horst, Ulrich: Mean-field leader-follower games with terminal state constraint (2020)
  3. Mebirouk, AbdelMouemin; Bouheroum-Mentri, Sabria; Aceto, Lidia: Approximation of eigenvalues of Sturm-Liouville problems defined on a semi-infinite domain (2020)
  4. Horst, Ulrich; Xia, Xiaonyu: Multi-dimensional optimal trade execution under stochastic resilience (2019)
  5. Budd, Chris; Koch, Othmar; Taghizadeh, Leila; Weinmüller, Ewa: Asymptotic properties of the space-time adaptive numerical solution of a nonlinear heat equation (2018)
  6. Putkaradze, Vakhtang; Rogers, Stuart: Constraint control of nonholonomic mechanical systems (2018)
  7. Burkotová, Jana; Rachunková, Irena; Weinmüller, Ewa B.: On singular BVPs with nonsmooth data: convergence of the collocation schemes (2017)
  8. Graewe, Paulwin; Horst, Ulrich: Optimal trade execution with instantaneous price impact and stochastic resilience (2017)
  9. Li, Lin; Lin, Ping; Si, Xinhui; Zheng, Liancun: A numerical study for multiple solutions of a singular boundary value problem arising from laminar flow in a porous pipe with moving wall (2017)
  10. Lima, P. M.; Morgado, M. L.; Schöbinger, M.; Weinmüller, E. B.: A novel computational approach to singular free boundary problems in ordinary differential equations (2017)
  11. Feichtinger, Anna; Makaruk, Aleksander; Weinmüller, Ewa; Friedl, Anton; Harasek, Michael: Collocation method for the modeling of membrane gas permeation systems (2015)
  12. Gerdts, Matthias: A survey on optimal control problems with differential-algebraic equations (2015)
  13. 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)
  14. Burkotová, Jana; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa B.: On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity (2014)
  15. Gschwindl, Jürgen; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa B.: Positive blow-up solutions of nonlinear models from real world dynamics (2014)
  16. 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)
  17. 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)
  18. Hastermann, G.; Lima, P. M.; Morgado, M. L.; Weinmüller, E. B.: Density profile equation with (p)-Laplacian: analysis and numerical simulation (2013)
  19. 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)
  20. Rachůnková, Irena; Spielauer, Alexander; Staněk, Svatoslav; Weinmüller, Ewa B.: Positive solutions of nonlinear Dirichlet BVPs in ODEs with time and space singularities (2013)

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