An accurate spectral collocation method for nonlinear systems of fractional differential equations and related integral equations with nonsmooth solutions
MA Zaky - Applied Numerical Mathematics, 2020 - Elsevier
This paper aims to provide a rigorous analysis of exponential convergence of an adaptive
spectral collocation method for a general nonlinear system of rational-order fractional initial …
spectral collocation method for a general nonlinear system of rational-order fractional initial …
Collocation methods for Volterra integral and integro-differential equations: A review
We present a collection of recent results on the numerical approximation of Volterra integral
equations and integro-differential equations by means of collocation type methods, which …
equations and integro-differential equations by means of collocation type methods, which …
Multivalue collocation methods for ordinary and fractional differential equations
The present paper illustrates some classes of multivalue methods for the numerical solution
of ordinary and fractional differential equations. In particular, it focuses on two-step and …
of ordinary and fractional differential equations. In particular, it focuses on two-step and …
A multistep Legendre--Gauss spectral collocation method for nonlinear Volterra integral equations
We introduce a multistep Legendre--Gauss spectral collocation method for the nonlinear
Volterra integral equations of the second kind. This method is easy to implement and …
Volterra integral equations of the second kind. This method is easy to implement and …
[PDF][PDF] On the stability of ϑ-methods for stochastic Volterra integral equations
D Conte, R D'Ambrosio, B Paternoster - Discr. Cont. Dyn. Sys …, 2018 - academia.edu
The paper is focused on the analysis of stability properties of a family of numerical methods
designed for the numerical solution of stochastic Volterra integral equations. Stability …
designed for the numerical solution of stochastic Volterra integral equations. Stability …
Stability analysis of spline collocation methods for fractional differential equations
This paper deals with spline collocation methods for fractional differential equations,
introduced by Pedas and Tamme (2014). Some practical formulas are derived, for the …
introduced by Pedas and Tamme (2014). Some practical formulas are derived, for the …
Lagrange collocation method for solving Volterra–Fredholm integral equations
K Wang, Q Wang - Applied Mathematics and Computation, 2013 - Elsevier
In this paper, the Lagrange collocation method is used to solve the Volterra–Fredholm
integral equations. This method transforms the system of the linear integral equations into …
integral equations. This method transforms the system of the linear integral equations into …
Multistep collocation methods for Volterra integro-differential equations
Multistep collocation methods for Volterra integro-differential equations are derived and
analyzed. They increase the order of convergence of classical one-step collocation …
analyzed. They increase the order of convergence of classical one-step collocation …
Multistep collocation methods for integral-algebraic equations with non-vanishing delays
In this article, we study the piecewise multistep collocation method for a class of functional
integral equations with non-vanishing delays. Based on the notions of the tractability index …
integral equations with non-vanishing delays. Based on the notions of the tractability index …
High order exponentially fitted methods for Volterra integral equations with periodic solution
A Cardone, R D'Ambrosio, B Paternoster - Applied Numerical Mathematics, 2017 - Elsevier
The present paper illustrates the construction of direct quadrature methods of arbitrary order
for Volterra integral equations with periodic solution. The coefficients of these methods …
for Volterra integral equations with periodic solution. The coefficients of these methods …