Jacobi spectral Galerkin method for the integrated forms of second-order differential equations

DOI10.1016/j.amc.2010.08.006zbMath1204.65132OpenAlexW2003412273MaRDI QIDQ606838

S. I. El-Soubhy, Ali H. Bhrawy

Publication date: 18 November 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.08.006

zbMATH Keywords

numerical resultsDirichlet problemsJacobi polynomialsPoisson equationspectral-Galerkin methodlinear elliptic differential equations

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (8)

A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations ⋮ A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals ⋮ A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions ⋮ Jacobi pseudo-spectral method JPSM and BPES for solving differential equations ⋮ A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations ⋮ New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method ⋮ On Jacobi polynomials and fractional spectral functions on compact symmetric spaces ⋮ Descriptions of fractional coefficients of Jacobi polynomial expansions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials
• Jacobi spectral Galerkin method for elliptic Neumann problems
• Spectral methods with sparse matrices
• Spectral approximation for elliptic boundary value problems
• The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
• Galerkin spectral method for the vorticity and stream function equations
• On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations
• The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function
• Jacobi spectral method for differential equations with rough asymptotic behaviors at infinity
• Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials
• The special functions and their approximations. Vol. I, II
• On the Coefficients of Integrated Expansions of Ultraspherical Polynomials
• A Jacobi spectral Galerkin method for the integrated forms of fourth‐order elliptic differential equations
• Improved Condition Number for Spectral Methods
• 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
• Explicit Formulae for the Coefficients of Integrated Expansions of Jacobi Polynomials and Their Integrals
• On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials
• On the coefficients of differentiated expansions and derivatives of Jacobi polynomials
• Efficient spectral-Galerkin algorithms for direct solution of the integrated forms of second-order equations using ultraspherical polynomials
• On Direct Methods for Solving Poisson’s Equations

This page was built for publication: Jacobi spectral Galerkin method for the integrated forms of second-order differential equations