Abstract
Nonlocality and spatial heterogeneity of many practical systems have made fractional differential equations very useful tools in Science and Engineering. However, solving these type of models is computationally demanding. In this paper, we propose an exponential integrator method for space fractional models as an attractive and easy-to-code alternative for other existing second-order exponential integrator methods. This scheme is based on using a real distinct poles discretization for the underlying matrix exponentials. One of the major benefits of the proposed scheme is that the algorithm could be easily implemented in parallel to take advantage of multiple processors for increased computational efficiency. The scheme is established to be second-order convergent; and proven to be robust for nonlinear space fractional reaction–diffusion problems involving non-smooth initial data. Our approach is exhibited by solving a system of two-dimensional problems which exhibits pattern formation and has applications in cell-division. Empirically, super-diffusion processes are displayed by investigating the effect of the fractional power of the underlying Laplacian operator on the pattern formation found in these models. Furthermore, the superiority of our method over competing second order ETD schemes, BDF2 scheme, and IMEX schemes is demonstrated.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.