Abstract
In this paper, we give our first attempt to implement a localized collocation method, namely Generalized Finite Difference Method (GFDM), for the Turing patterns formation problems on smooth, closed, connected surfaces of codimension one embedded in R3. Based on projections from surface differential operators to Euclidean differential operators, the surface PDEs in extrinsic form are given explicitly and could be solved directly by GFDM only using a set of collocation points distributed on surfaces. A sparse system formed from localization scheme makes it efficient for solving long time evolution Turing patterns formation problems. Numerical demonstrations including convergence test, Turing spot and stripe problems are provided to illustrate its potentiality.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
