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References from An Improved Spectral-Element Method for the High-Dimensional Spatial Fourth-Order Differential Equations with Temporal Fractional Derivative. Local targets link to admitted publications; unresolved targets remain external evidence.
Fourth-order partial differential equations for image enhancement
2006 · External reference
An adaptive approach for solving fourth-order partial differential equations: Algorithm and applications to engineering models
10.1007/s40314-022-02125-5 · 2022 · External reference
Reduced proper orthogonal decomposition spectral element method for the solution of 2D multi-term time fractional mixed diffusion and diffusion-wave equations in linear and nonlinear modes
10.1016/j.camwa.2022.02.016 · 2022 · External reference
An efficient localized meshless Fourier method for nonlinear fourth-order fractional integro-differential equations
10.1016/j.camwa.2026.05.028 · 2026 · External reference
The least squares spectral element method for the Cahn-Hilliard equation
10.1016/j.apm.2010.07.034 · 2011 · External reference
The comparison of three meshless methods using radial basis functions for solving fourth-order partial differential equations
10.1016/j.enganabound.2010.03.004 · 2010 · External reference
The optimal convergence of a modified weak Galerkin spectral element method for second order elliptic equations
10.1007/s40314-025-03200-3 · 2025 · External reference
Spectral method and spectral element method for three dimensional linear elliptic system: Analysis and application
10.1007/s10915-020-01145-9 · 2020 · External reference
The Legendre Galerkin spectral element method for the generalized Rosenau-type equations
10.1007/s12190-024-02349-0 · 2025 · External reference
An expanded mixed finite element method for fourth-order hyperbolic equations with variable coefficients
10.1016/j.cam.2025.117305 · 2026 · External reference
A two-grid mixed finite element method for an onlinear fourth-order reaction–diffusion problem with time-fractional derivative
10.1016/j.camwa.2015.09.012 · 2015 · External reference
Fully Petrov-Galerkin spectral method for the distributed-order time-fractional fourth-order partial differential equation
10.1007/s00366-020-00968-2 · 2021 · External reference
Galerkin spectral and finite difference methods for the solution of fourth-order time fractional partial integro-differential equation with a weakly singular kernel
10.1007/s12190-024-02173-6 · 2024 · External reference
Numerical analysis of the quadratic spline collocation method and averaged L1 scheme on graded mesh for nonlinear time-fractional fourth-order reaction-diffusion problem
10.1002/num.70004 · 2025 · External reference
Conforming finite element method for the time-fractional nonlinear stochastic fourth-order reaction diffusion equation
10.1002/num.23020 · 2023 · External reference
A computationally efficient numerical scheme for the solution of fourth-order time-fractional partial integro-differential equation
10.1007/s13540-025-00423-3 · 2025 · External reference
Efficient spectral-element methods in polar coordinates for complex geometries with piecewise-smooth boundaries
10.1137/24m1702441 · 2025 · External reference
Direct meshless local Petrov-Galerkin (DMLPG) method for time-fractional fourth-order reaction-diffusion problem on complex domains
10.1016/j.camwa.2019.08.001 · 2020 · External reference
Legendre spectral element method for solving time fractional modified anomalous sub-diffusion equation
10.1016/j.apm.2015.10.036 · 2016 · External reference
Nonuniform L1/spectral element algorithm for the time fractional diffusion equation
10.1016/j.matcom.2025.05.025 · 2026 · External reference
Space-time nonconforming least squares spectral element approximation for parabolic PDEs with corner singularity
10.1007/s10915-026-03238-3 · 2026 · External reference
Exponentially accurate spectral element method for fourth order elliptic problems
10.1007/s10915-016-0300-z · 2017 · External reference
Numerical solution of 2D distributed-order fractional cable equation on regular and irregular domains based on the spectral element method
10.1080/00207160.2025.2575092 · 2026 · External reference
Computational study based on the Laplace transform and local discontinuous galerkin methods for solving fourth-order time-fractional partial integro-differential equations with weakly singular kernels
10.1007/s40314-024-02813-4 · 2024 · External reference
Efficient Legendre spectral and spectral element methods for second-order problems with diagonalization technique
10.1007/s10915-025-03048-z · 2025 · External reference
An improved finite difference and Galerkin spectral method for the fourth-order time fractional partial differential equations
10.3934/math.20251202 · 2025 · External reference
Legendre-Galerkin spectral-element method for the biharmonic equations and its applications
10.1016/j.camwa.2017.07.039 · 2017 · External reference
Finite difference/spectral approximations for the time-fractional diffusion equation
10.1016/j.jcp.2007.02.001 · 2007 · External reference
Accuracy of spectral element method for wave, parabolic and Schrödinger equations
10.1137/21m1401760 · 2022 · External reference
Conforming finite element method for the time-fractional nonlinear stochastic fourth-order reaction diffusion equation
10.1002/num.23020 · ExternalCitation · doi-reference
Numerical analysis of the quadratic spline collocation method and averaged L1 scheme on graded mesh for nonlinear time-fractional fourth-order reaction-diffusion problem
10.1002/num.70004 · ExternalCitation · doi-reference
Fully Petrov-Galerkin spectral method for the distributed-order time-fractional fourth-order partial differential equation
10.1007/s00366-020-00968-2 · ExternalCitation · doi-reference
Exponentially accurate spectral element method for fourth order elliptic problems
10.1007/s10915-016-0300-z · ExternalCitation · doi-reference
Spectral method and spectral element method for three dimensional linear elliptic system: Analysis and application
10.1007/s10915-020-01145-9 · ExternalCitation · doi-reference
Efficient Legendre spectral and spectral element methods for second-order problems with diagonalization technique
10.1007/s10915-025-03048-z · ExternalCitation · doi-reference
Space-time nonconforming least squares spectral element approximation for parabolic PDEs with corner singularity
10.1007/s10915-026-03238-3 · ExternalCitation · doi-reference
Galerkin spectral and finite difference methods for the solution of fourth-order time fractional partial integro-differential equation with a weakly singular kernel
10.1007/s12190-024-02173-6 · ExternalCitation · doi-reference
The Legendre Galerkin spectral element method for the generalized Rosenau-type equations
10.1007/s12190-024-02349-0 · ExternalCitation · doi-reference
A computationally efficient numerical scheme for the solution of fourth-order time-fractional partial integro-differential equation
10.1007/s13540-025-00423-3 · ExternalCitation · doi-reference
An adaptive approach for solving fourth-order partial differential equations: Algorithm and applications to engineering models
10.1007/s40314-022-02125-5 · ExternalCitation · doi-reference
Computational study based on the Laplace transform and local discontinuous galerkin methods for solving fourth-order time-fractional partial integro-differential equations with weakly singular kernels
10.1007/s40314-024-02813-4 · ExternalCitation · doi-reference
The optimal convergence of a modified weak Galerkin spectral element method for second order elliptic equations
10.1007/s40314-025-03200-3 · ExternalCitation · doi-reference
The least squares spectral element method for the Cahn-Hilliard equation
10.1016/j.apm.2010.07.034 · ExternalCitation · doi-reference
Legendre spectral element method for solving time fractional modified anomalous sub-diffusion equation
10.1016/j.apm.2015.10.036 · ExternalCitation · doi-reference
An expanded mixed finite element method for fourth-order hyperbolic equations with variable coefficients
10.1016/j.cam.2025.117305 · ExternalCitation · doi-reference
A two-grid mixed finite element method for an onlinear fourth-order reaction–diffusion problem with time-fractional derivative
10.1016/j.camwa.2015.09.012 · ExternalCitation · doi-reference
Legendre-Galerkin spectral-element method for the biharmonic equations and its applications
10.1016/j.camwa.2017.07.039 · ExternalCitation · doi-reference
Direct meshless local Petrov-Galerkin (DMLPG) method for time-fractional fourth-order reaction-diffusion problem on complex domains
10.1016/j.camwa.2019.08.001 · ExternalCitation · doi-reference
Reduced proper orthogonal decomposition spectral element method for the solution of 2D multi-term time fractional mixed diffusion and diffusion-wave equations in linear and nonlinear modes
10.1016/j.camwa.2022.02.016 · ExternalCitation · doi-reference
An efficient localized meshless Fourier method for nonlinear fourth-order fractional integro-differential equations
10.1016/j.camwa.2026.05.028 · ExternalCitation · doi-reference
The comparison of three meshless methods using radial basis functions for solving fourth-order partial differential equations
10.1016/j.enganabound.2010.03.004 · ExternalCitation · doi-reference
Finite difference/spectral approximations for the time-fractional diffusion equation
10.1016/j.jcp.2007.02.001 · ExternalCitation · doi-reference
Nonuniform L1/spectral element algorithm for the time fractional diffusion equation
10.1016/j.matcom.2025.05.025 · ExternalCitation · doi-reference
Numerical solution of 2D distributed-order fractional cable equation on regular and irregular domains based on the spectral element method
10.1080/00207160.2025.2575092 · ExternalCitation · doi-reference
Accuracy of spectral element method for wave, parabolic and Schrödinger equations
10.1137/21m1401760 · ExternalCitation · doi-reference
Efficient spectral-element methods in polar coordinates for complex geometries with piecewise-smooth boundaries
10.1137/24m1702441 · ExternalCitation · doi-reference
An improved finite difference and Galerkin spectral method for the fourth-order time fractional partial differential equations
10.3934/math.20251202 · ExternalCitation · doi-reference
