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 …

Multistep collocation methods for Volterra integral equations

D Conte, B Paternoster - Applied numerical mathematics, 2009 - Elsevier
We introduce multistep collocation methods for the numerical integration of Volterra Integral
Equations, which depend on the numerical solution in a fixed number of previous time steps …

Rapid variable-step computation of dynamic convolutions and Volterra-type integro-differential equations: RK45 Fehlberg, RK4

MN Azese - Heliyon, 2024 - cell.com
We introduce a novel, time-efficient adaptive Runge-Kutta computational scheme tailored for
systematically solving linear and nonlinear Volterra-type Integro-Differential Equations …

[HTML][HTML] Explicit methods based on barycentric rational interpolants for solving non-stiff Volterra integral equations

A Abdi, JP Berrut, SA Hosseini - Applied Numerical Mathematics, 2022 - Elsevier
For their high accuracy and good stability properties, implicit numerical methods are widely
used for solving Volterra integral equations, while, in order to save computational effort …

Multistep collocation methods for Volterra integro-differential equations

A Cardone, D Conte - Applied Mathematics and Computation, 2013 - Elsevier
Multistep collocation methods for Volterra integro-differential equations are derived and
analyzed. They increase the order of convergence of classical one-step collocation …

[HTML][HTML] On a method for solving a two-dimensional nonlinear integral equation of the second kind

MA Abdou, AA Badr, MB Soliman - Journal of computational and applied …, 2011 - Elsevier
In this article, the existence of at least one solution of a nonlinear integral equation of the
second kind is proved. The degenerate method is used to obtain a nonlinear algebraic …

A high-order predictor-corrector method for solving nonlinear differential equations of fractional order

TB Nguyen, B Jang - Fractional Calculus and applied analysis, 2017 - degruyter.com
An accurate and efficient new class of predictor-corrector schemes are proposed for solving
nonlinear differential equations of fractional order. By introducing a new prediction method …

Two-step diagonally-implicit collocation based methods for Volterra integral equations

D Conte, R DʼAmbrosio, B Paternoster - Applied Numerical Mathematics, 2012 - Elsevier
We introduce a family of diagonally-implicit continuous methods for the numerical integration
of Volterra Integral Equations. The derived methods are characterized by a lower triangular …

Singular integral equations of convolution type with Cauchy kernel in the class of exponentially increasing functions

P Li - Applied Mathematics and Computation, 2019 - Elsevier
In this paper we study some classes of generalized singular integral equations of
convolution type with Cauchy kernel in the class of exponentially increasing functions. Such …

An interpolation-based method for solving Volterra integral equations

N Karamollahi, M Heydari, GB Loghmani - Journal of Applied Mathematics …, 2022 - Springer
In this study, the second kind Volterra integral equations (VIEs) are considered. An algorithm
based on the two-point Taylor formula as a special case of the Hermite interpolation is …