Spectral Methods: Algorithms, Analysis and Applications

By Jie Shen, Tao Tang, Lilian Wang. 2011

1,868 citations recorded by the source corpus.

Subfields: Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4e02f0ac5780a8b3b2232e532a68629ac3854bbf

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Citations in the corpus

• Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind (2012, neutral): “, [21].”
• The phase field method for geometric moving interfaces and their numerical approximations (2019, methodology): “For problems defined on regular computational domains but not with periodic boundary conditions, other spectral implementations are possible such as Chebyshev spectral methods for Dirichlet boundary conditions, see discussions in the following books and recent surveys [65, 85, 235, 242, 318, 378, 56”
• A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation (2014, methodology): “The explicit formula of the Jacobi polynomial is stated as follows [37]:”
• Numerical Approaches to Fractional Integrals and Derivatives: A Review (2020, methodology): “with {xk} k=0 and {ωk} N k=0 being the collocation points and the corresponding quadrature weights [43].”
• Well-posedness and numerical algorithm for the tempered fractional differential equations (2019, methodology): “0 as the weight function; {z j} N j=0 and {ωj} N j=0 are the (N +1)-degree Jacobi-Gauss-Lobatto nodes and their corresponding Jacobi weights in the reference interval [−1,1], respectively; see, e.g., [38]. Now we turn to describe the computational scheme for Eq. (63). For this purpose, we define a gr”
• Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations (2016, background): “The continuity and coercivity of the bilinear form a(·, ·) is shown in [20] (Lemma 3.”
• Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line (2014, positive): “Then we have uNðxÞ ¼ XN j¼0 ajL ð Þ j ðxÞ: ð2:10Þ We will introduce the Laguerre–Gauss-type quadratures, including Laguerre–Gauss and Laguerre–Gauss– Radau (Shen et al., 2011).”
• Gegenbauer spectral method for time‐fractional convection–diffusion equations with variable coefficients (2015, background): “The Gegenbauer polynomials satisfy the following orthogonality relation [47] Z 1”