A Unified Spectral Method for FPDEs with Two-sided Derivatives; Stability, and Error Analysis

Abstract

We present the stability and error analysis of the unified Petrov-Galerkin spectral method, developed in \cite{samiee2017Unified}, for linear fractional partial differential equations with two-sided derivatives and constant coefficients in any ($1+d$)-dimensional space-time hypercube, $d=1,2,3,\cdots$, subject to homogeneous Dirichlet initial/boundary conditions. Specifically, we prove the existence and uniqueness of the weak form and perform the corresponding stability and error analysis of the proposed method. Finally, we perform several numerical simulations to compare the theoretical and computational rates of convergence.

References in corpus (3)

• A second-order numerical method for two-dimensional two-sided space fractional convection diffusion equation
• A Petrov-Galerkin Spectral Element Method for Fractional Elliptic Problems
• A Unified Spectral Method for FPDEs with Two-sided Derivatives; A Fast Solver

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