Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations
View through CrossRef
A class of numerical methods is developed for second order
Volterra integro-differential equations by using
a Legendre spectral approach. We provide a rigorous error analysis
for the proposed methods, which shows that the numerical errors
decay exponentially in the $L^\infty$-norm and $L^2$-norm.
Numerical examples illustrate the convergence and effectiveness of
the numerical methods.
Global Science Press
Title: Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations
Description:
A class of numerical methods is developed for second order
Volterra integro-differential equations by using
a Legendre spectral approach.
We provide a rigorous error analysis
for the proposed methods, which shows that the numerical errors
decay exponentially in the $L^\infty$-norm and $L^2$-norm.
Numerical examples illustrate the convergence and effectiveness of
the numerical methods.
Related Results
Incidental Collocation Learning from Different Modes of Input and Factors That Affect Learning
Incidental Collocation Learning from Different Modes of Input and Factors That Affect Learning
Collocations, i.e., words that habitually co-occur in texts (e.g., strong coffee, heavy smoker), are ubiquitous in language and thus crucial for second/foreign language (L2) learne...
Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations
Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations
The key objective of this paper is to construct exact traveling wave solutions of the conformable time second integro-differential Kadomtsev–Petviashvili (KP) hierarchy equation us...
A Solution to the Kermack and McKendrick Integro-Differential Equations
A Solution to the Kermack and McKendrick Integro-Differential Equations
AbstractIn this manuscript, we derive a closed form solution to the full Kermack and McKendrick integro-differential equations (Kermack and McKendrick 1927) which we call the KMES....
Unbounded Star Convergence in Lattices
Unbounded Star Convergence in Lattices
Let L be a vector lattice, "(" x_α ") " be a L-valued net, and x∈L . If |x_α-x|∧u→┴o 0 for every u ∈〖 L〗_+ then it is said that the net "(" x_α ")" unbounded order converges ...
Numerical approximation of space-fractional diffusion equation using Laguerre spectral collocation method
Numerical approximation of space-fractional diffusion equation using Laguerre spectral collocation method
The space-fractional diffusion equation is extensively used to model various issues in engineering and mathematics. This paper addresses the numerical approximation of the space-fr...
An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels
An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels
This paper presents an $hp$-version Chebyshev spectral collocation method for
nonlinear Volterra integro-differential equations with weakly singular kernels. The $hp$-version error...
Spectral Petrov-Galerkin Methods for the Second Kind Volterra Type Integro-Differential Equations
Spectral Petrov-Galerkin Methods for the Second Kind Volterra Type Integro-Differential Equations
This work is to provide general spectral and pseudo-spectral
Jacobi-Petrov-Galerkin approaches for the second kind Volterra
integro-differential equations. The Gauss-Legendre quadr...
A Study for Solving Pseudo-Parabolic Viscous Diffusion, Telegraph, Poisson and Helmholtz PDE using Legendre-Collocation Method
A Study for Solving Pseudo-Parabolic Viscous Diffusion, Telegraph, Poisson and Helmholtz PDE using Legendre-Collocation Method
Legendre collocation approach is implemented employing the operative-differential array escorted by the shifted Legendre polynomials. The significance of the proposed approach is r...