Efficient spectral-Galerkin algorithms for direct solution of the integrated forms of second-order equations using ultraspherical polynomials

DOI10.1017/S1446181100003540zbMath1138.65104OpenAlexW2019622682MaRDI QIDQ5437204

Eid H. Doha, Ali H. Bhrawy

Publication date: 18 January 2008

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446181100003540

zbMATH Keywords

algorithmsHelmholtz equationPoisson equationultraspherical polynomialsspectral-Galerkin methodsecond-order elliptic differential equationsultraspherical-Galerkin methods

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (13)

Jacobi spectral Galerkin method for the integrated forms of second-order differential equations ⋮ Highly accurate method for boundary value problems with Robin boundary conditions ⋮ Matrix decomposition algorithms for elliptic boundary value problems: A survey ⋮ Efficient spectral-Petrov-Galerkin methods for the integrated forms of third- and fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials ⋮ A Jacobi-Jacobi dual-Petrov-Galerkin method for third- and fifth-order differential equations ⋮ Matrix decomposition algorithms for arbitrary order \(C^0\) tensor product finite element systems ⋮ A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals ⋮ A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations ⋮ Efficient spectral ultraspherical-Galerkin algorithms for the direct solution of 2nth-order linear differential equations ⋮ Numerical solutions of odd order linear and nonlinear initial value problems using a shifted Jacobi spectral approximations ⋮ Efficient spectral ultraspherical-dual-Petrov-Galerkin algorithms for the direct solution of \((2n + 1)\)th-order linear differential equations ⋮ A Jacobi spectral Galerkin method for the integrated forms of fourth‐order elliptic differential equations ⋮ Jacobi spectral Galerkin method for elliptic Neumann problems

Cites Work

• Unnamed Item
• The coefficients of differentiated expansions and derivatives of ultraspherical polynomials
• An accurate solution of parabolic equations by expansion in ultraspherical polynomials
• Spectral methods with sparse matrices
• Spectral methods for problems in complex geometries
• Algebraic spectral multigrid methods
• The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
• Gegenbauer approximation and its applications to differential equations on the whole line
• On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations
• An accurate solution of the Poisson equation by the Chebyshev-tau method
• The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function
• The special functions and their approximations. Vol. I, II
• On the Coefficients of Integrated Expansions of Ultraspherical Polynomials
• Improved Condition Number for Spectral Methods
• Spectral Methods and Their Applications
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials
• Efficient Spectral-Galerkin Algorithms for Direct Solution of Second-Order Equations Using Ultraspherical Polynomials
• On Direct Methods for Solving Poisson’s Equations

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