Müntz pseudo-spectral method: theory and numerical experiments

DOI10.1016/j.cnsns.2020.105510zbMath1453.65358arXiv1908.02306OpenAlexW3082670824MaRDI QIDQ2212036

M. R. Eslahchi, Hassan Khosravian-Arab

Publication date: 17 November 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.02306

zbMATH Keywords

error boundsorthogonal projectionsfractional ordinary and partial differential equationsnon-classical interpolants

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Spectral theory; eigenvalue problems on manifolds (58C40) Fractional ordinary differential equations (34A08) Fractional partial differential equations (35R11)

Related Items (2)

Müntz Sturm-Liouville problems: theory and numerical experiments ⋮ A generalization of Müntz-Legendre polynomials and its implementation in optimal control of nonlinear fractional delay systems

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractional spectral collocation methods for linear and nonlinear variable order FPDEs
• Fractional calculus for scientists and engineers.
• A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations
• Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials
• Fractional Sturm-Liouville boundary value problems in unbounded domains: theory and applications
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• An efficient technique based on finite difference/finite element method for solution of two-dimensional space/multi-time fractional Bloch-Torrey equations
• A unified Petrov-Galerkin spectral method for fractional PDEs
• A pseudospectral method for fractional optimal control problems
• Fully spectral collocation method for nonlinear parabolic partial integro-differential equations
• A review of applications of fractional calculus in Earth system dynamics
• A Müntz-collocation spectral method for weakly singular Volterra integral equations
• Fractional-order uniaxial visco-elasto-plastic models for structural analysis
• A Petrov-Galerkin spectral element method for fractional elliptic problems
• Error estimate of finite element/finite difference technique for solution of two-dimensional weakly singular integro-partial differential equation with space and time fractional derivatives
• Fractional spectral and pseudo-spectral methods in unbounded domains: theory and applications
• Stochastic smoothed profile method for modeling random roughness in flow problems
• Optimal Fractional Integration Preconditioning and Error Analysis of Fractional Collocation Method Using Nodal Generalized Jacobi Functions
• A Generalized Spectral Collocation Method with Tunable Accuracy for Fractional Differential Equations with End-Point Singularities
• Spectral Methods
• Spectral Methods for Time-Dependent Problems
• The Eigenvalues of Second-Order Spectral Differentiation Matrices
• Spectral Methods in MATLAB
• A Legendre spectral element method (SEM) based on the modified bases for solving neutral delay distributed‐order fractional damped diffusion‐wave equation
• A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
• Application of the dual reciprocity boundary integral equation approach to solve fourth-order time-fractional partial differential equations
• Solving nonlinear fractional partial differential equations using the homotopy analysis method
• Fractional differentiation matrices with applications
• Fractional Calculus with Applications for Nuclear Reactor Dynamics
• Spectral Methods
• Fractional Spectral Collocation Method
• Fractional Calculus with Applications in Mechanics
• Stochastic models for fractional calculus

This page was built for publication: Müntz pseudo-spectral method: theory and numerical experiments