MINDS: Guest speaker Master student Thomas Rooijakkers
Title
Computer-assisted validation of solutions to differential-algebraic systems in systems biology
Abstract
Today, computer simulations are a vital tool in the mathematical analysis of dynamical systems. Simulations allow people to imagine the, often complex, dynamics of (nonlinear) systems. Besides being a great tool for inspiration, simulations can also be used to test and reject hypotheses. Making those numerical computations rigourous truly unleashes the power of numerics.
In this thesis, we consider the validation of numerically computed solutions to differential-algebraic systems in the domain of systems biology. We treat a particular toy model of the qORAC framework, in the form of a semi-explicit differential-algebraic system, to illustrate a computer-assisted validation technique that proves the existence of an exact, and unique solution to the dynamical system, within a range of the numerically computed solution.
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