Workgroup on Numerics of Evolution Equations, Stiff and Singular Problems

Research interests Auzinger

The activities of the workgroup comprise analysis and implementation of numerical integration algorithms for ODE systems and some classes of PDEs. The main focus is on evolution equations, stiff systems and singular and impulsive boundary value problems. Analysis of error structures, development of practical error estimators and adaptive integration are major issues. All this includes software development and the solution of various problems arising in applications.

Undergraduate Student Assistant

Research interests Schranz-Kirlinger

Numerical Analysis, Numerical Solution of Differential Equations, Biomathematics

Research interests Weinmüller

The main research focus is on numerical methods for classes of ODEs and DAEs relevant for applications especially singular and stiff problems that arise when studying e.g. turbulent flows, reaction-diffusion systems, nonlinear optics models, and shallow water phenomena. The research concentrates on the error analysis and the design of reliable algorithms. The techniques also apply to certain types of PDEs, which under self-similar transformation reduce to ODEs with singularities. The group has expertise in the numerical analysis and simulation for ODEs, DAEs, and PDEs, collocation methods, error control, adaptivity, and software development.