Müntz--Galerkin Methods and Applications to Mixed Dirichlet--Neumann Boundary Value Problems

DOI10.1137/15M1052391zbMath1416.65482MaRDI QIDQ3186114

Yingwei Wang, Jie Shen

Publication date: 8 August 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

error estimatesingular solutionspectral-Galerkin methodMüntz polynomial

Mathematics Subject Classification ID

Related Items (25)

A new computational method based on fractional Lagrange functions to solve multi-term fractional differential equations ⋮ Nontensorial generalised hermite spectral methods for PDEs with fractional Laplacian and Schrödinger operators ⋮ An efficient collocation method with convergence rates based on Müntz spaces for solving nonlinear fractional two-point boundary value problems ⋮ Enriched spectral methods and applications to problems with weakly singular solutions ⋮ Novel spectral methods for Schrödinger equations with an inverse square potential on the whole space ⋮ A fractional spectral method with applications to some singular problems ⋮ A new direct method for solving optimal control problem of nonlinear Volterra-Fredholm integral equation via the Müntz-Legendre polynomials ⋮ An efficient spectral method for solving third-kind Volterra integral equations with non-smooth solutions ⋮ High order hybrid asymptotic augmented finite volume methods for nonlinear degenerate wave equations ⋮ Fast structured Jacobi-Jacobi transforms ⋮ New fractional pseudospectral methods with accurate convergence rates for fractional differential equations ⋮ Enriched spectral method for stiff convection-dominated equations ⋮ Stable evaluations of fractional derivative of the Müntz-Legendre polynomials and application to fractional differential equations ⋮ Semi-decoupling hybrid asymptotic and augmented finite volume method for nonlinear singular interface problems ⋮ Numerical solution of Volterra-Fredholm integral equations using the collocation method based on a special form of the Müntz-Legendre polynomials ⋮ The high order augmented finite volume methods based on series expansion for nonlinear degenerate parabolic equations ⋮ A new spectral method using nonstandard singular basis functions for time-fractional differential equations ⋮ Müntz Sturm-Liouville problems: theory and numerical experiments ⋮ A novel Petrov-Galerkin method for a class of linear systems of fractional differential equations ⋮ New spectral element method for Volterra integral equations with weakly singular kernel ⋮ Numerical solution of a class of fractional order integro-differential algebraic equations using Müntz-Jacobi tau method ⋮ On the rate of convergence of spectral collocation methods for nonlinear multi-order fractional initial value problems ⋮ A new operational matrix based on Müntz-Legendre polynomials for solving distributed order fractional differential equations ⋮ New fractional Lanczos vector polynomials and their application to system of Abel-Volterra integral equations and fractional differential equations ⋮ A fractional version of the recursive tau method for solving a general class of Abel-Volterra integral equations systems

Cites Work

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• Stable generalized finite element method (SGFEM)
• Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials
• Generalized Jacobi polynomials/functions and their applications
• Singularities and treatments of elliptic boundary value problems.
• Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond
• Optimal spectral-Galerkin methods using generalized Jacobi polynomials
• Treatment of singularities in Helmholtz-type equations using the boundary element method
• Spectral Methods
• The extended/generalized finite element method: An overview of the method and its applications
• Muntz type Theorems I
• Design of quadrature rules for Müntz and Müntz-logarithmic polynomials using monomial transformation
• Muntz Systems and Orthogonal Muntz-Legendre Polynomials
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries
• Convergence of Adaptive Finite Element Methods
• Spectral Methods
• The treatment of singularities of partial differential equations by relaxation methods
• Asymptotic behavior of Müntz orthogonal polynomials

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