Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Jie Shen,Purdue University and Xiamen University
Inviter:
Haijun Yu
Title:
Efficient and accurate spectral methods for solving a class of fractional PDEs
Time & Venue:
2015.6.12 10:00-11:00am Z311
Abstract:
We consider spectral approximations of PDEs with two-sided fractional derivatives. For the PDEs with Riesz derivatives, we construct spectral methods using special basis functions based on generalized Jacobi functions which lead to diagonal systems, and we derive rigorous error estimates which show that the convergence rate is of spectral type in properly weighted Sobolev spaces despite the fact that the solutions have singularities at the endpoints. For PDEs with more general two-sided fractional derivatives, we construct efficient spectral-element methods with geometric mesh to achieve spectral accuracy. We shall also discuss how to solve multi-dimensional fractional PDEs with spectral methods.
Appendix：
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