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 11 articles , 1 standard article )

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  1. Burkotová, Jana; Rachůnková, Irena; Staněk, Svatoslav; Weinmüller, Ewa B.: On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity (2014)
  2. 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)
  3. Koch, Othmar; März, Roswitha; Praetorius, Dirk; Weinmüller, Ewa: Collocation methods for index 1 DAEs with a singularity of the first kind (2010)
  4. Cash, J.; Kitzhofer, G.; Koch, O.; Moore, G.; Weinmüller, E.: Numerical solution of singular two point BVPs (2009)
  5. Auzinger, Winfried; Koch, Othmar; Praetorius, Dirk; Weinmüller, Ewa: New a posteriori error estimates for singular boundary value problems (2005)
  6. Auzinger, Winfried; Koch, Othmar; Weinmüller, Ewa: Analysis of a new error estimate for collocation methods applied to singular boundary value problems (2005)
  7. Auzinger, W.; Koch, O.; Weinmüller, E.: Efficient mesh selection for collocation methods applied to singular BVPs (2005)
  8. Koch, Othmar: Asymptotically correct error estimation for collocation methods applied to singular boundary value problems (2005)
  9. Koch, Othmar; Weinmüller, Ewa: Analytical and numerical treatment of a singular initial value problem in avalanche modeling. (2004)
  10. Koch, Othmar; Weinmüller, Ewa B.: The convergence of shooting methods for singular boundary value problems (2003)
  11. Koch, Othmar; Weinmüller, Ewa B.: Iterated defect correction for the solution of singular initial value problems (2001)