×

avalanche.f

swMATH ID: 13859
Software Authors: Koch, Othmar; Weinmüller, Ewa
Description: 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.
Homepage: http://www.asc.tuwien.ac.at/~ewa/
Keywords: Singular initial value problem; Existence of solution; Numerical solution; Implicit; Euler method; Iterated defect correction; Leading-edge model; Avalanche run-out
Related Software: bvpsuite; Sbvp; COLSYS; bvp4c; Matlab; COLNEW; RODAS; RADAU; RWPM
Cited in: 22 Documents

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Analytical and numerical treatment of a singular initial value problem in avalanche modeling. Zbl 1089.34004
Koch, Othmar; Weinmüller, Ewa
2004
all top 5

Cited by 31 Authors

14 Weinmüller, Ewa B.
10 Koch, Othmar
5 Burkotová, Jana
5 Rachůnková, Irena
4 Auzinger, Winfried
2 Cao, Wanrong
2 Deng, Nan
2 Kamrul Hasan, M.
2 März, Roswitha
2 Praetorius, Dirk
2 Shamsul Alam, Mohammad
2 Staněk, Svatoslav
1 Ahamed, Md. Suzan
1 Ali, Md. Ayub
1 Arqub, Omar Abu
1 Auer, Felix Karl
1 Cash, Jeff R.
1 Datsko, B. Yo.
1 Dick, Alexander
1 Haque, B. M. Ikramul
1 Hossain, Md Bellal
1 Kitzhofer, Georg
1 Kunynets’, A. V.
1 Kutniv, Myroslav V.
1 Moore, Gerald
1 Pang, Guofei
1 Rahaman, Md. Habibur
1 Wang, Huiru
1 Włoch, Andrzej
1 Wurm, Stefan
1 Zhang, Chengjian
all top 5

Cited in 13 Serials

4 Applied Numerical Mathematics
3 Mathematics of Computation
3 Journal of Computational and Applied Mathematics
2 SIAM Journal on Numerical Analysis
1 Applied Mathematics and Computation
1 BIT
1 Calcolo
1 Numerische Mathematik
1 Numerical Algorithms
1 Mathematical Problems in Engineering
1 Boundary Value Problems
1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics
1 Applied Mathematics and Nonlinear Sciences
all top 5

Cited in 7 Fields

22 Numerical analysis (65-XX)
16 Ordinary differential equations (34-XX)
1 Partial differential equations (35-XX)
1 Probability theory and stochastic processes (60-XX)
1 Statistics (62-XX)
1 Mechanics of deformable solids (74-XX)
1 Geophysics (86-XX)

Citations by Year