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

Lubomir Banas, Herbert Dawid, Tsiry Avisoa Randrianasolo, Johannes Storn, Xingang Wen

Research output: Contribution to journalArticleResearchpeer-review


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.
Original languageEnglish
Article number54
Pages (from-to)92.2022
Number of pages35
JournalJournal of Scientific Computing
Publication statusE-pub ahead of print - 4 Jul 2022

Cite this