Előadó: Csomós Petra (ELTE, Alkalmazott Analízis és Számításmatematika Tanszék)

 

Innovative Integrators

Abstract: Innovative integrators (operator splitting procedures, exponential integrators, and Magnus-type integrators) provide an efficient way to approximate the solution of nonlinear evolution equations. The lecture gives a first insight into the topic. We will introduce the various innovative integrators, show what kind of equations they are designed for, and sketch how to prove their convergence. We also consider an error estimation of the total numerical method, i.e., when innovative integrators are applied together with space and time discretization schemes. Since the study of evolution equations requires a functional analytic framework, we briefly recall the corresponding results in operator semigroup theory. As an application, we present our results on computing the optimal state in linear quadratic regulator problems, especially in the case of shallow water equations.

 

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