Large scale scientific computing
Large scale scientific computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Numerical methods and software for sensitivity analysis of differential-algebraic systems
Applied Numerical Mathematics
Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software
Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software
Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation
Applied Numerical Mathematics
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The mathematical modelling of a special modular catalytic reactor kit leads to a system of partial differential equation in two space dimensions. As customary, this model contains uncertain physical parameters, which may be adapted to fit experimental data. To solve this nonlinear least-squares problem we apply a damped Gauss-Newton method. A method of lines approach is used to evaluate the associated model equations. By an a priori spatial discretization, a large DAE system is derived and integrated with an adaptive, linearly implicit extrapolation method. For sensitivity evaluation we apply an internal numerical differentiation technique, which reuses linear algebra information from the model integration. In order not to interfere with the control of the Gauss-Newton iteration these computations are done usually very accurately and, therefore, with substantial cost. To overcome this difficulty, we discuss several accuracy adaptation strategies, e.g., a master-slave mode. Finally, we present some numerical experiments.