An optimized Crank–Nicolson finite difference extrapolating model for the fractional-order parabolic-type sine-Gordon equation

A reduced proper orthogonal decomposition (POD) element free Galerkin (POD-EFG) method to simulate two-dimensional solute transport problems and error estimate

(2018) Mehdi Dehghan et al.   APPLIED NUMERICAL MATHEMATICS

A combination of proper orthogonal decomposition–discrete empirical interpolation method (POD–DEIM) and meshless local RBF-DQ approach for prevention of groundwater contamination

(2018) Mehdi Dehghan et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation

(2018) Mehdi Dehghan et al.   ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

A reduced-order extrapolating Crank-Nicolson finite difference scheme for the Riesz space fractional order equations with a nonlinear source function and delay

(2018) Yanhua Cao et al.   Journal of Nonlinear Sciences and Applications

The use of proper orthogonal decomposition (POD) meshless RBF-FD technique to simulate the shallow water equations

(2017) Mehdi Dehghan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A POD-based-optimized finite difference CN-extrapolated implicit scheme for the 2D viscoelastic wave equation †

(2017) Hong Xia et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

A POD reduced-order finite difference time-domain extrapolating scheme for the 2D Maxwell equations in a lossy medium

(2016) Zhendong Luo et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

A reduced-order finite difference extrapolation algorithm based on POD technique for the non-stationary Navier–Stokes equations

(2012) Zhendong Luo et al.   APPLIED MATHEMATICAL MODELLING

A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem

(2011) Zhendong Luo et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

A reduced finite element formulation based on POD method for two-dimensional solute transport problems

(2011) Zhendong Luo et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

A reduced finite volume element formulation and numerical simulations based on POD for parabolic problems

(2010) Zhendong Luo et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Nonlinear Model Reduction via Discrete Empirical Interpolation

(2010) Saifon Chaturantabut et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Some reduced finite difference schemes based on a proper orthogonal decomposition technique for parabolic equations

(2009) Ping Sun et al.   APPLIED NUMERICAL MATHEMATICS

A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation

(2008) Zhendong Luo et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Mixed Finite Element Formulation and Error Estimates Based on Proper Orthogonal Decomposition for the Nonstationary Navier–Stokes Equations

(2008) Zhendong Luo et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS