Numerical Approximation of a System of Hamilton–Jacobi–Bellman Equations Arising in Innovation Dynamics

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Authors

External Organisational units

  • Universität Bielefeld

Abstract

We consider a system of fully nonlinear partial differential equations that corresponds to the Hamilton–Jacobi–Bellman equations for the value functions of an optimal innovation investment problem of a monopoly firm facing bankruptcy risk. We compare several algorithms for the numerical solution of the considered problem: the collocation method, the finite difference method, WENO method and the adaptive finite element method. We discuss implementation issues for the considered schemes and perform numerical studies for different model parameters to assess their performance.

Details

Original languageEnglish
Article number54
Pages (from-to)92.2022
Number of pages35
JournalJournal of Scientific Computing
Volume92.2022
DOIs
Publication statusPublished - 4 Jul 2022