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Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
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Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows
inferred← citeshttps://doi.org/10.1007/s11424-011-8016-5openalex-snapshot
A Legendre Galerkin spectral method for optimal control problems
inferred← citeshttps://doi.org/10.1007/s11425-016-0280-5openalex-snapshot
Efficient splitting schemes for magneto-hydrodynamic equations
inferred← citeshttps://doi.org/10.1007/s11425-022-2094-xopenalex-snapshot
An accurate and efficient space-time Galerkin spectral method for the subdiffusion equation
inferred← citeshttps://doi.org/10.1007/s11464-013-0271-4openalex-snapshot
Generalized Jacobi-Gauss-Lobatto interpolation
inferred← citeshttps://doi.org/10.1007/s11741-008-0103-3openalex-snapshot
Legendre expansion method for Helmholz equations
inferred← citeshttps://doi.org/10.1007/s12190-020-01494-6openalex-snapshot
A Legendre reproducing kernel method with higher convergence order for a class of singular two-point boundary value problems
inferred← citeshttps://doi.org/10.1007/s12190-024-02173-6openalex-snapshot
Galerkin spectral and finite difference methods for the solution of fourth-order time fractional partial integro-differential equation with a weakly singular kernel
inferred← citeshttps://doi.org/10.1007/s12190-025-02602-0openalex-snapshot
Pseudo-spectral second kind Chebyshev polynomials differentiation matrices for solving high-order nonlinear differential equations
inferred← citeshttps://doi.org/10.1007/s12190-026-02890-0openalex-snapshot
A spectral-Galerkin method for the level set equation of power mean curvature flow
inferred← citeshttps://doi.org/10.1007/s40096-019-0292-6openalex-snapshot
A computational approach for solving fractional integral equations based on Legendre collocation method
inferred← citeshttps://doi.org/10.1007/s40096-022-00488-8openalex-snapshot
Numerical solutions of two-dimensional PDE-constrained optimal control problems via bilinear pseudo-spectral method
inferred← citeshttps://doi.org/10.1007/s40304-021-00278-zopenalex-snapshot
Efficient Fully Discrete Spectral-Galerkin Scheme for the Volume-Conserved Multi-Vesicular Phase-Field Model of Lipid Vesicles with Adhesion Potential
inferred← citeshttps://doi.org/10.1007/s40324-016-0079-8openalex-snapshot
An efficient technique for finding the eigenvalues and the eigenelements of fourth-order Sturm-Liouville problems
inferred← citeshttps://doi.org/10.1007/s42967-019-00012-1openalex-snapshot
A New Spectral Method Using Nonstandard Singular Basis Functions for Time-Fractional Differential Equations
inferred← citeshttps://doi.org/10.1007/s42967-019-00016-xopenalex-snapshot
Jacobi–Sobolev Orthogonal Polynomials and Spectral Methods for Elliptic Boundary Value Problems
inferred← citeshttps://doi.org/10.1007/s42967-019-0004-0openalex-snapshot
Unconditionally Stable Pressure-Correction Schemes for a Nonlinear Fluid-Structure Interaction Model
inferred← citeshttps://doi.org/10.1007/s42967-019-00041-wopenalex-snapshot
$$C^1$$-Conforming Quadrilateral Spectral Element Method for Fourth-Order Equations
inferred← citeshttps://doi.org/10.1007/s42967-020-00060-yopenalex-snapshot
Second-Order Finite Difference/Spectral Element Formulation for Solving the Fractional Advection-Diffusion Equation
inferred← citeshttps://doi.org/10.1016/b978-008043944-0/50938-0openalex-snapshot
Simulation of the differentially heated 8: 1 rectangular cavity by a Galerkin-Legendre spectral projection method
inferred← citeshttps://doi.org/10.1016/j.acha.2009.12.002openalex-snapshot
A new generalization of the PSWFs with applications to spectral approximations on quasi-uniform grids
inferred← citeshttps://doi.org/10.1016/j.amc.2008.09.038openalex-snapshot
Approximate solution of the Sturm–Liouville problems with Legendre–Galerkin–Chebyshev collocation method
inferred← citeshttps://doi.org/10.1016/j.amc.2010.08.006openalex-snapshot
Jacobi spectral Galerkin method for the integrated forms of second-order differential equations
inferred← citeshttps://doi.org/10.1016/j.amc.2011.08.107openalex-snapshot
A Legendre spectral-element method for the one-dimensional fourth-order equations
inferred← citeshttps://doi.org/10.1016/j.amc.2014.01.157openalex-snapshot
Numerical approximation of a nonlinear fourth-order integro-differential equation by spectral method
inferred← citeshttps://doi.org/10.1016/j.amc.2014.06.057openalex-snapshot
Legendre–Galerkin method for the linear Fredholm integro-differential equations
inferred← citeshttps://doi.org/10.1016/j.amc.2014.08.086openalex-snapshot
Sinc-Galerkin method for solving biharmonic problems
inferred← citeshttps://doi.org/10.1016/j.amc.2015.06.082openalex-snapshot
Error estimates of spectral Legendre–Galerkin methods for the fourth-order equation in one dimension
inferred← citeshttps://doi.org/10.1016/j.amc.2017.11.024openalex-snapshot
Two-dimensional shifted Legendre polynomials operational matrix method for solving the two-dimensional integral equations of fractional order
inferred← citeshttps://doi.org/10.1016/j.amc.2017.12.009openalex-snapshot
High-order implicit Galerkin–Legendre spectral method for the two-dimensional Schrödinger equation
inferred← citeshttps://doi.org/10.1016/j.amc.2018.12.050openalex-snapshot
Space-time spectral method for the Cattaneo equation with time fractional derivative
inferred← citeshttps://doi.org/10.1016/j.amc.2019.03.045openalex-snapshot
Non-polynomial spline approach in two-dimensional fractional sub-diffusion problems
inferred← citeshttps://doi.org/10.1016/j.aml.2004.07.028openalex-snapshot
A fourth-order eigenvalue problem arising in viscoelastic flow
inferred← citeshttps://doi.org/10.1016/j.aml.2016.04.005openalex-snapshot
The a posteriori error estimates of Chebyshev–Petrov–Galerkin methods for second-order equations
inferred← citeshttps://doi.org/10.1016/j.apm.2008.05.005openalex-snapshot
Efficient spectral ultraspherical-Galerkin algorithms for the direct solution of 2nth-order linear differential equations
inferred← citeshttps://doi.org/10.1016/j.apm.2011.07.059openalex-snapshot
Chebyshev–Legendre pseudo-spectral method for the generalised Burgers–Fisher equation
inferred← citeshttps://doi.org/10.1016/j.apm.2012.04.015openalex-snapshot
Chebyshev tau meshless method based on the highest derivative for fourth order equations
inferred← citeshttps://doi.org/10.1016/j.apnum.2005.11.009openalex-snapshot
A Legendre spectral method in time for first-order hyperbolic equations
inferred← citeshttps://doi.org/10.1016/j.apnum.2006.07.012openalex-snapshot
Fourierization of the Legendre–Galerkin method and a new space–time spectral method
inferred← citeshttps://doi.org/10.1016/j.apnum.2007.07.001openalex-snapshot
Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials
inferred← citeshttps://doi.org/10.1016/j.apnum.2008.01.003openalex-snapshot
Efficient spectral-Galerkin methods for polar and cylindrical geometries
inferred← citeshttps://doi.org/10.1016/j.apnum.2008.04.003openalex-snapshot
Generalized Jacobi polynomials/functions and their applications
inferred← citeshttps://doi.org/10.1016/j.apnum.2008.07.004openalex-snapshot
Spectral methods in linear stability. Applications to thermal convection with variable gravity field
inferred← citeshttps://doi.org/10.1016/j.apnum.2012.03.004openalex-snapshot
Jacobi spectral method with essential imposition of Neumann boundary condition
inferred← citeshttps://doi.org/10.1016/j.apnum.2014.05.010openalex-snapshot
Parallel spectral-element direction splitting method for incompressible Navier–Stokes equations
inferred← citeshttps://doi.org/10.1016/j.apnum.2015.01.010openalex-snapshot
Mixed spectral method for heat transfer with inhomogeneous Neumann boundary condition in an infinite strip
inferred← citeshttps://doi.org/10.1016/j.apnum.2015.11.007openalex-snapshot
A Legendre–Galerkin spectral approximation and estimation of the index of refraction for transmission eigenvalues
inferred← citeshttps://doi.org/10.1016/j.apnum.2017.02.006openalex-snapshot
Numerical study of an adaptive domain decomposition algorithm based on Chebyshev tau method for solving singular perturbed problems
inferred← citeshttps://doi.org/10.1016/j.apnum.2017.03.009openalex-snapshot
Spectral element technique for nonlinear fractional evolution equation, stability and convergence analysis
inferred← citeshttps://doi.org/10.1016/j.apnum.2018.01.003openalex-snapshot
Diagonalized Legendre spectral methods using Sobolev orthogonal polynomials for elliptic boundary value problems
inferred← citeshttps://doi.org/10.1016/j.apnum.2018.01.011openalex-snapshot
Modal spectral element method in curvilinear domains
inferred← citeshttps://doi.org/10.1016/j.apnum.2018.04.012openalex-snapshot
The spectral-Galerkin approximation of nonlinear eigenvalue problems
inferred← citeshttps://doi.org/10.1016/j.apnum.2018.07.001openalex-snapshot
A novel finite difference discrete scheme for the time fractional diffusion-wave equation
inferred← citeshttps://doi.org/10.1016/j.apnum.2019.10.016openalex-snapshot
Inverse matrices for pseudospectral differentiation operators in polar coordinates by stepwise integrations and low-rank updates
inferred← citeshttps://doi.org/10.1016/j.apnum.2020.05.025openalex-snapshot
A spectral method for solving nonhomogeneous Neumann boundary value problems on quadrilaterals
inferred← citeshttps://doi.org/10.1016/j.apnum.2020.07.004openalex-snapshot
Multidomain pseudospectral integration preconditioning matrices for the advection and the diffusion operators
inferred← citeshttps://doi.org/10.1016/j.apnum.2022.06.013openalex-snapshot
Logarithmic Jacobi collocation method for Caputo–Hadamard fractional differential equations
inferred← citeshttps://doi.org/10.1016/j.apnum.2022.11.024openalex-snapshot
Numerical algorithm for a generalized form of Schnakenberg reaction-diffusion model with gene expression time delay
inferred← citeshttps://doi.org/10.1016/j.apnum.2023.02.014openalex-snapshot
A two-grid spectral method to study of dynamics of dense discrete systems governed by Rosenau-Burgers' equation
inferred← citeshttps://doi.org/10.1016/j.apnum.2023.07.018openalex-snapshot
Superconvergent postprocessing of the C1-conforming finite element method for fourth-order boundary value problems
inferred← citeshttps://doi.org/10.1016/j.apnum.2024.06.021openalex-snapshot
Energetic spectral-element time marching methods for phase-field nonlinear gradient systems
inferred← citeshttps://doi.org/10.1016/j.apnum.2024.09.028openalex-snapshot
Spectral-Galerkin methods for the fully nonlinear Monge-Ampère equation
inferred← citeshttps://doi.org/10.1016/j.apnum.2025.08.005openalex-snapshot
A biharmonic solver based on Fourier extension with oversampling technique for arbitrary domain
inferred← citeshttps://doi.org/10.1016/j.automatica.2026.113254openalex-snapshot
Splitting-up method for Zakai equation with α-Stable Lévy noise: Convergence analysis and applications to nonlinear filtering problems
inferred← citeshttps://doi.org/10.1016/j.cam.2005.06.011openalex-snapshot
A Legendre spectral element method for eigenvalues in hydrodynamic stability
inferred← citeshttps://doi.org/10.1016/j.cam.2009.01.025openalex-snapshot
A rational spectral method for the KdV equation on the half line
inferred← citeshttps://doi.org/10.1016/j.cam.2009.12.014openalex-snapshot
Numerical solution of the Poisson equation over hypercubes using reduced Chebyshev polynomial bases
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