A fast Galerkin-spectral method based on discrete Legendre polynomials for solving parabolic differential equation

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Related Items (1)

Chebyshev polynomial derivative-based spectral tau approach for solving high-order differential equations

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Some numerical algorithms for solving the highly oscillatory second-order initial value problems
Numerical solution of two-dimensional sine-Gordon and MBE models using Fourier spectral and high order explicit time stepping methods
Analyzing two-dimensional sine-Gordon equation with the mesh-free reproducing kernel particle Ritz method
Legendre spectral collocation in space and time for PDEs
High-order compact solution of the one-dimensional heat and advection-diffusion equations
Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)
High order compact alternating direction implicit method for the generalized sine-Gordon equation
Efficient space-time Legendre rational spectral method for parabolic problems in unbounded domains
The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation
Meshless local Petrov-Galerkin (MLPG) approximation to the two dimensional sine-Gordon equation
Fourierization of the Legendre-Galerkin method and a new space-time spectral method
Racah polynomials and recoupling schemes of $\mathfrak{su}(1,1)$
A Chebyshev spectral collocation method for solving Burgers'-type equations
Meshless local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity
Spectral collocation methods
Single and multi-interval Legendre $\tau$-methods in time for parabolic equations
Exponential Runge-Kutta methods for parabolic problems.
A Hahn computational operational method for variable order fractional mobile-immobile advection-dispersion equation
Exceptional Meixner and Laguerre orthogonal polynomials
Shifted Legendre reproducing kernel Galerkin method for the quasilinear degenerate parabolic problem
A RBF-WENO finite difference scheme for non-linear degenerate parabolic equations
A new solution for optimal control of fractional convection-reaction-diffusion equation using rational barycentric interpolation
Orthonormal shifted discrete Legendre polynomials for solving a coupled system of nonlinear variable-order time fractional reaction-advection-diffusion equations
The solution of the two-dimensional sine-Gordon equation using the method of lines
A uniformly convergent difference method for singularly perturbed parabolic partial differential equations with large delay and integral boundary condition
Space-time spectral method for two-dimensional semilinear parabolic equations
Spectral Methods in Time for Parabolic Problems
Dual $-1$ Hahn polynomials: “Classical” polynomials beyond the Leonard duality
Numerical approach for solving two dimensional fractal-fractional PDEs using peridynamic method
Space–time spectral collocation method for one-dimensional PDE constrained optimisation
Order‐Optimal Preconditioners for Implicit Runge–Kutta Schemes Applied to Parabolic PDEs
Galerkin Finite Element Methods for Parabolic Problems
Multigrid Methods for Implicit Runge--Kutta and Boundary Value Method Discretizations of Parabolic PDEs
Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations
An interpolation method for the optimal control problem governed by the elliptic convection–diffusion equation
An artificial neural network‐based method for the optimal control problem governed by the fractional parabolic equation
Optimal control of time-fractional convection-diffusion-reaction problem employing compact integrated RBF method
Improved training of physics-informed neural networks for parabolic differential equations with sharply perturbed initial conditions
A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations
A comparative approach for time-delay fractional optimal control problems: discrete versus continuous Chebyshev polynomials

This page was built for publication: A fast Galerkin-spectral method based on discrete Legendre polynomials for solving parabolic differential equation