On the use of Domain-Theoretic Derivatives for Solving ODEs
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Dirk Pattinson (Imperial)

(Joint work with A. Oomatia)

Second order methods for solving ordinary differential equations
(ODEs) standardly require the differentiability of the vector field
that defines the equation. Here, we show that replacing the
classical derivative with the domain theoretic derivative allows us
to use a second order method even if the vector field defining the
equation is Lipschitz but not differentiable. Working in a
domain-theoretic framework, this leads to a new algorithm for
solving ODEs with guaranteed error bounds that is applicable to
problems that lie outside the domain of other verified ODE solvers.
In addition to the mathematical theory,  we report on our
experiences with an implementation of this new method and
demonstrate its superiority by means of experimental data.