Research Interests and Projects of F.E.Cellier Concerning the Mixed Symbolic and Numerical Solution of DAE Systems

1. Development of a New Class of Implicit F-stable Single-step Methods for the Numerical Solution of Marginally Stable ODE Systems (1992-1994)

2. Development of a Simulator for the Assessment of Breakdown Behavior of Reverse-biased Power Transistors (1985-1989)

3. Development of Adaptive Algorithms for Compensation of Atmospherical Disturbances in the Control of Active Optical Telescopes (1988-1991)

4. Development of Algorithms for the Numerical Treatment of Discontinuities in ODE Models (1974-1979)

5. Development of Algorithms for the Simulation of Marginally Stable Electronic Circuits in Spice (1989-1991)

6. Development of Algorithms for the Symbolic Preprocessing of DAE Systems for the Purpose of Improving Their Numerical Properties at Simulation Run Time (1995-2005)

7. Development of Implicit Linear Differentiation Algorithms for the Numerical Simulation of Non-linear Electronic Circuits in Spice (1989-1991)

8. Development of Implicit Linear High-order Multi-step Methods for the Numerical Solution of Stiff ODE Systems (1992-1994)

9. Development of Methods for Radiation Hardening of Power Transistors under the Influence of Total Dose Ionizing Radiation (1987-1992)

10. Development of Stiffly-stable Step-size Control Algorithms for Fully Implicit Runge-Kutta Algorithms of the Radau and Lobatto Classes, as well as for Diagonally Implicit SDIRK Algorithms (2000-2005)

11. Development of Symbolic Index Reduction Algorithms for the Simulation of Structurally Singular DAE Systems with Discontinuities (1995-2005)
12. Simulation and Adaptive Control of Electrical Discharge Machinery for Die Sinking Work (1972-1976)

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