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Koch, Othmar; Weinmüller, Ewa

Analytical and numerical treatment of a singular initial value problem in avalanche modeling. (English) Zbl 1089.34004

Appl. Math. Comput. 148, No. 2, 561-570 (2004).
Summary: 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.

Cited in 19 Documents

MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
74L05 Geophysical solid mechanics
86A60 Geological problems

Keywords:

Singular initial value problem; Existence of solution; Numerical solution; Implicit; Euler method; Iterated defect correction; Leading-edge model; Avalanche run-out

Software:

avalanche.f
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Full Text: DOI

References:

[1] D.M. McClung, O. Hungr, An equation for calculating snow avalanche run-up against barriers, in: Avalanche Formation, Movement and Effects, IAHS Publ. no. 162, 1987, pp. 605-612; D.M. McClung, O. Hungr, An equation for calculating snow avalanche run-up against barriers, in: Avalanche Formation, Movement and Effects, IAHS Publ. no. 162, 1987, pp. 605-612
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[7] W. Auzinger, O. Koch, P. Kofler, E. Weinmüller, The application of shooting to singular boundary value problems, Techn. Rep. Nr. 126/99, Inst. for Appl. Math. and Numer. Anal., Vienna Univ. of Technology, Austria, available at http://fsmat.at/ othmar/research.html; W. Auzinger, O. Koch, P. Kofler, E. Weinmüller, The application of shooting to singular boundary value problems, Techn. Rep. Nr. 126/99, Inst. for Appl. Math. and Numer. Anal., Vienna Univ. of Technology, Austria, available at http://fsmat.at/ othmar/research.html
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