High-order integral nodal discontinuous Gegenbauer-Galerkin method for solving viscous Burgers' equation
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Publication:5031734
DOI10.1080/00207160.2018.1554860OpenAlexW2902035786MaRDI QIDQ5031734
Bülent Karasözen, Kareem T. Elgindy
Publication date: 16 February 2022
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207160.2018.1554860
Burgers' equationGegenbauer polynomialsdiscontinuous Galerkinbarycentricintegration matrixGegenbauer-Gauss
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Roundoff error (65G50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Approximation by polynomials (41A10) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)
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High-order numerical solution of viscous Burgers' equation using an extended Cole–Hopf barycentric Gegenbauer integral pseudospectral method, A stabilized FEM formulation with discontinuity-capturing for solving Burgers'-type equations at high Reynolds numbers
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Cites Work
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- A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation.
- Numerical solution of Burgers' equation by cubic Hermite collocation method
- Numerical solution of the coupled viscous Burgers equations by Chebyshev-Legendre pseudo-spectral method
- Numerical solution of Burgers' equation with modified cubic B-spline differential quadrature method
- A hybrid numerical scheme for the numerical solution of the Burgers' equation
- The local discontinuous Galerkin finite element method for Burger's equation
- Numerical solutions of nonlinear Burgers equation with modified cubic B-splines collocation method
- Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices
- A Haar wavelet quasilinearization approach for numerical simulation of Burgers' equation
- Spectral integration of linear boundary value problems
- The complex Burgers equation as a model for collinear interactions of weakly nonlinear shear plane waves in anisotropic elastic materials
- The variational homotopy perturbation method for solving \(((n\times n)+1)\) dimensional Burgers' equations
- A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers' equation
- High-order, stable, and efficient pseudospectral method using barycentric Gegenbauer quadratures
- Wavelet based preconditioners for sparse linear systems
- Numerical solution of the Burgers' equation by automatic differentiation
- Some implicit methods for the numerical solution of Burgers' equation
- Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations
- A sixth-order compact finite difference scheme to the numerical solutions of Burgers' equation
- Generation of higher order pseudospectral integration matrices
- Efficient and stable generation of higher-order pseudospectral integration matrices
- Efficient numerical techniques for Burgers' equation
- An approximation method for solving Burgers' equation using Legendre wavelets
- Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted Gegenbauer integral pseudospectral method
- Moving mesh discontinuous Galerkin methods for PDEs with traveling waves
- An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers' equation
- Numerical solution of turbulence problems by solving Burgers' equation
- Optimization via Chebyshev polynomials
- High-order shifted Gegenbauer integral pseudo-spectral method for solving differential equations of Lane-Emden type
- A numerical solution of Burgers' equation by modified Adomian method
- The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations
- Optimal Gegenbauer quadrature over arbitrary integration nodes
- Polynomial based differential quadrature method for numerical solution of nonlinear Burgers equation
- A finite element multigrid preconditioner for Chebyshev-collocation methods
- Variational multiscale element-free Galerkin method combined with the moving Kriging interpolation for solving some partial differential equations with discontinuous solutions
- Variable shape parameter strategy in local radial basis functions collocation method for solving the 2D nonlinear coupled Burgers' equations
- A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers' equation
- Fast, accurate, and small-scale direct trajectory optimization using a Gegenbauer transcription method
- High-order numerical solution of second-order one-dimensional hyperbolic telegraph equation using a shifted Gegenbauer pseudospectral method
- A Fast and Well-Conditioned Spectral Method
- Optimal boundary control of the unsteady Burgers equation with simultaneous space-time discretization
- A differential quadrature method for numerical solutions of Burgers'‐type equations
- A Staggered Discontinuous Galerkin Method with Local TV Regularization for the Burgers Equation
- Implicit time integration of hyperbolic conservation laws via discontinuous Galerkin methods
- Spectral Integration and Two-Point Boundary Value Problems
- Integration Preconditioning Matrix for Ultraspherical Pseudospectral Operators
- Costate approximation in optimal control using integral Gaussian quadrature orthogonal collocation methods
- Implementing Spectral Methods for Partial Differential Equations
- A Preconditioning Matrix for the Chebyshev Differencing Operator
- An Instability Phenomenon in Spectral Methods
- Integration Preconditioning of Pseudospectral Operators. I. Basic Linear Operators
- A Collocation Solution For Burgers Equation Using Quadratic B-Spline Finite Elements
- A differential quadrature based numerical method for highly accurate solutions of Burgers' equation
- The numerical stability of barycentric Lagrange interpolation
- Accuracy and Stability of Numerical Algorithms
- An efficient spectral method for ordinary differential equations with rational function coefficients
- High-order adaptive Gegenbauer integral spectral element method for solving non-linear optimal control problems
- On Preconditioned Iterative Methods for Burgers Equations
- A Probabilistic Approach to a Solution of Nonlinear Parabolic Equations
- Chebyshev Solution of Differential, Integral and Integro-Differential Equations
- Application of polynomial preconditioners to conservation laws
