avalanche.f

Analytical and numerical treatment of a singular initial value problem in avalanche modeling. We discuss a leading-edge model used in the computation of the run-out length of dry-flowing avalanches. The model has the form of a singular initial value problem for a scalar ordinary differential equation describing the avalanche dynamics. Existence, uniqueness and smoothness properties of the analytical solution are shown. We also prove the existence of a unique root of the solution. Moreover, we present a FORTRAN 90 code for the numerical computation of the run-out length. The code is based on a solver for singular initial value problems which is an implementation of the acceleration technique known as iterated defect correction based on the implicit Euler method.


References in zbMATH (referenced in 18 articles , 1 standard article )

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  1. Kutniv, M. V.; Datsko, B. Y.; Kunynets, A. V.; Włoch, A.: A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations (2020)
  2. Burkotová, Jana; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa B.; Wurm, Stefan: On nonlinear singular BVPs with nonsmooth data. I: Analytical results (2018)
  3. Wang, Huiru; Zhang, Chengjian: The adapted block boundary value methods for singular initial value problems (2018)
  4. Burkotová, Jana; Rachunková, Irena; Weinmüller, Ewa B.: On singular BVPs with nonsmooth data: analysis of the linear case with variable coefficient matrix (2017)
  5. Burkotová, Jana; Rachunková, Irena; Weinmüller, Ewa B.: On singular BVPs with nonsmooth data: convergence of the collocation schemes (2017)
  6. Hasan, M. Kamrul; Ahamed, M. Suzan; Haque, B. M. Ikramul; Alam, M. S.; Hossain, M. Bellal: A higher order implicit method for numerical solution of singular initial value problems (2017)
  7. Abu Arqub, Omar: Reproducing kernel algorithm for the analytical-numerical solutions of nonlinear systems of singular periodic boundary value problems (2015)
  8. Burkotová, Jana; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa B.: On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity (2014)
  9. 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)
  10. Koch, Othmar; März, Roswitha; Praetorius, Dirk; Weinmüller, Ewa: Collocation methods for index 1 DAEs with a singularity of the first kind (2010)
  11. Cash, J.; Kitzhofer, G.; Koch, O.; Moore, G.; Weinmüller, E.: Numerical solution of singular two point BVPs (2009)
  12. Auzinger, Winfried; Koch, Othmar; Praetorius, Dirk; Weinmüller, Ewa: New a posteriori error estimates for singular boundary value problems (2005)
  13. Auzinger, Winfried; Koch, Othmar; Weinmüller, Ewa: Analysis of a new error estimate for collocation methods applied to singular boundary value problems (2005)
  14. Auzinger, W.; Koch, O.; Weinmüller, E.: Efficient mesh selection for collocation methods applied to singular BVPs (2005)
  15. Koch, Othmar: Asymptotically correct error estimation for collocation methods applied to singular boundary value problems (2005)
  16. Koch, Othmar; Weinmüller, Ewa: Analytical and numerical treatment of a singular initial value problem in avalanche modeling. (2004)
  17. Koch, Othmar; Weinmüller, Ewa B.: The convergence of shooting methods for singular boundary value problems (2003)
  18. Koch, Othmar; Weinmüller, Ewa B.: Iterated defect correction for the solution of singular initial value problems (2001)