Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs, Second Edition

Dear Colleagues,

Fractional PDEs (FPDEs) generalize the classic (integer-order) calculus and PDEs to any differential form of fractional orders. FPDEs are emerging as a powerful tool for modeling challenging multiscale phenomena, including overlapping microscopic and macroscopic scales, anomalous transport and long-range time–memory or spatial interactions. However, the exact solutions of FPDEs cannot be explicitly expressed; thus, numerical methods based on various spatial and temporal discretizations have become the mainstream tools for such FPDEs and have experienced a drastic development in recent decades. These spatial and temporal discretizations that maintain the important characteristics or structures of FPDEs, such as weak singularity, optimal long-time decay rate, long-term numerical stability and the convergence of numerical schemes for such FPDEs, are still limited. Therefore, developing efficient spatial and temporal discretizations for the numerical solutions of FPDEs remains challenging in the field of numerical analysis.

This Special Issue, titled “Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs, Second Edition”, will provide a platform for recent and original research results on efficient numerical methods for solving FPDEs. We invite authors to contribute original research articles on topics including, but not limited to, the following:

• Finite difference, finite elements, finite volume and spectral methods;
• Nonuniform and adaptive discretizations;
• Adaptive space–time methods;
• Numerical treatments of integro-differential equations;
• Parallel-in-time methods;
• Fast matrix computations arising from numerical methods for FPDEs;
• Nonlocal modeling and computation;
• Convolution quadrature;
• Modeling and simulations involving (fractional) PDEs.

Dr. Xian-Ming Gu
Prof. Dr. Hongbin Chen
Prof. Dr. Xiangcheng Zheng
Guest Editors

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