Crank-Nicolson and Legendre spectral collocation methods for a partial integro-differential equation with a singular kernel

DOI10.1016/j.cam.2018.09.034zbMath1408.65074OpenAlexW2895751964WikidataQ115359805 ScholiaQ115359805MaRDI QIDQ1713101

Akbar Mohebbi

Publication date: 24 January 2019

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

Full work available at URL: https://doi.org/10.1016/j.cam.2018.09.034

zbMATH Keywords

stabilityconvergencesingular kernelpartial integro-differential equationLegendre spectral collocation

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical quadrature and cubature formulas (65D32) Integro-partial differential equations (35R09)

Related Items

On regularity and stability for a class of nonlocal evolution equations with nonlinear perturbations, Stability analysis for a class of semilinear nonlocal evolution equations, A Crank-Nicolson-type compact difference method with the uniform time step for a class of weakly singular parabolic integro-differential equations, A second-order accurate Crank-Nicolson finite difference method on uniform meshes for nonlinear partial integro-differential equations with weakly singular kernels, Study of the backward difference and local discontinuous Galerkin (LDG) methods for solving fourth-order partial integro-differential equations (PIDEs) with memory terms: stability analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Quasi wavelet based numerical method for a class of partial integro-differential equation
• An implicit/explicit spectral method for Burgers' equation
• New conservative difference schemes for a coupled nonlinear Schrödinger system
• Legendre spectral collocation method for the solution of the model describing biological species living together
• Spectral methods for weakly singular Volterra integral equations with smooth solutions
• A finite difference scheme for partial integro-differential equations with a weakly singular kernel
• An integrodifferential equation for rigid heat conductors with memory
• Three methods based on the interpolation scaling functions and the mixed collocation finite difference schemes for the numerical solution of the nonlinear generalized Burgers-Huxley equation
• A compact difference scheme for a partial integro-differential equation with a weakly singular kernel
• Space-time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains
• A general theory of heat conduction with finite wave speeds
• Spectral Methods
• Solution of a partial integro-differential equation arising from viscoelasticity
• Numerical solution of fourth-order integro-differential equations using Chebyshev cardinal functions
• Approximation Results for Orthogonal Polynomials in Sobolev Spaces
• Mixed finite difference and Galerkin methods for solving Burgers equations using interpolating scaling functions