Sbvp 1.0 - a matlab solver for singular boundary value problems. We present a MATLAB package for boundary value problems in ordinary differential equations (ODEs). Our aim is the efficient numerical solution of systems of ODEs with a singularity of the first kind, but the solver can also be used for regular problems. The basic solution is computed using collocation methods and a new, efficient estimate of the global error is used for adaptive mesh selection. Here, we analyze some of the numerical aspects relevant for the implementation, describe measures to increase the efficiency of the code and compare its performance with the performance of established standard codes for boundary value problems.

References in zbMATH (referenced in 23 articles , 1 standard article )

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  1. Lamour, René; März, Roswitha; Weinmüller, Ewa: Boundary-value problems for differential-algebraic equations: A survey (2015)
  2. Coman, Ciprian D.; Liu, Xiang: Buckling-resistant thin annular plates in tension (2014)
  3. 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)
  4. Boisvert, Jason J.; Muir, Paul H.; Spiteri, Raymond J.: A Runge-Kutta BVODE solver with global error and defect control (2013)
  5. Capponi, Agostino; Cvitanić, Jakša; Yolcu, Türkay: Optimal contracting with effort and misvaluation (2013)
  6. Auzinger, Winfried; Lehner, Herbert; Weinmüller, Ewa: An efficient asymptotically correct error estimator for collocation solutions to singular index-1 DAEs (2011)
  7. Pulverer, Gernot; Söderlind, Gustaf; Weinmüller, Ewa: Automatic grid control in adaptive BVP solvers (2011)
  8. Koch, Othmar; März, Roswitha; Praetorius, Dirk; Weinmüller, Ewa: Collocation methods for index 1 DAEs with a singularity of the first kind (2010)
  9. Pulverer, Gernot; Staněk, Svatoslav; Weinmüller, Ewa B.: Analysis and numerical solutions of positive and dead core solutions of singular Sturm-Liouville problems (2010)
  10. Rachůnková, Irena; Pulverer, Gernot; Weinmüller, Ewa B.: A unified approach to singular problems arising in the membrane theory (2010)
  11. Jafri, Mahanum Diana; Suleiman, Mohamed; Majid, Zanariah Abdul; Ibrahim, Zarina Bibi: Solving directly two point boundary value problems using direct multistep method (2009)
  12. Karabay, Bilgehan; Pulverer, Gernot; Weinmüller, Ewa: Foreign ownership restrictions: a numerical approach (2009)
  13. 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)
  14. Rachunková, Irena; Koch, Othmar; Pulverer, Gernot; Weinmüller, Ewa: On a singular boundary value problem arising in the theory of shallow membrane caps (2007)
  15. Auzinger, Winfried; Karner, Ernst; Koch, Othmar; Weinmüller, Ewa: Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations (2006)
  16. Auzinger, Winfried; Koch, Othmar; Praetorius, Dirk; Weinmüller, Ewa: New a posteriori error estimates for singular boundary value problems (2005)
  17. Auzinger, Winfried; Koch, Othmar; Weinmüller, Ewa: Analysis of a new error estimate for collocation methods applied to singular boundary value problems (2005)
  18. Auzinger, W.; Koch, O.; Weinmüller, E.: Efficient mesh selection for collocation methods applied to singular BVPs (2005)
  19. Baganas, K.: Wave propagation and profile reconstruction in inhomogeneous elastic media (2005)
  20. Koch, Othmar: Asymptotically correct error estimation for collocation methods applied to singular boundary value problems (2005)

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