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Exponential Time Differencing for Nonlinear (Fractional) Diffusion-Reaction Systems

When: Monday, January 29, 2018
11:00 AM - 12:00 PM
Where: Textiles Building 105
Description: 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 talk, I will present a novel Exponential Time Differencing (ETD) scheme for nonlinear reaction-diffusion fractional models. This scheme is based on using a real distinct poles discretization for the underlying matrix exponentials. Due to these real distinct poles, the algorithm could be easily implemented in parallel to take advantage of multiple processors for increased computational efficiency. The method is established to be second order convergent; and proven to be robust for problems involving non-smooth or mismatched initial and boundary conditions and steep solution gradients. This scheme combined with fractional central differencing is used for simulating some nonlinear space fractional models. The superiority of the proposed ETD-RDP scheme over competing second-order ETD schemes and BDF2 scheme is demonstrated. The numerical tests show that the proposed scheme is computationally more efficient (in terms of cpu time).
Contact: EAS Seminar Series
Topical Areas: Faculty, Students, Students, Graduate, Students, Undergraduate, Mathematics