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Numerical Solution of Locally Loaded Volterra Integral Equations

Computation
Loaded Volterra integral equations represent a novel class of integral equations that have attracted considerable attention in recent years due to their numerous applications in various fields of science and engineering.
Vladislav Byankin, Aleksandr Tynda, Denis Sidorov, Aliona Dreglea   +3 more
doaj   +1 more source

Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity

Electronic Journal of Qualitative Theory of Differential Equations, 2017
The paper is devoted to the study of the solvability of a nonlinear Volterra–Stieltjes integral equation in the class of real functions defined, bounded and continuous on the real half-axis $\mathbb{R}_+$ and having finite limits at infinity.
Jozef Banas, Agnieszka Dubiel
doaj   +1 more source

Approximate solutions to several classes of Volterra and Fredholm integral equations using the neural network algorithm based on the sine-cosine basis function and extreme learning machine

Frontiers in Computational Neuroscience, 2023
In this study, we investigate a new neural network method to solve Volterra and Fredholm integral equations based on the sine-cosine basis function and extreme learning machine (ELM) algorithm.
Yanfei Lu, Shiqing Zhang, Futian Weng, Hongli Sun   +3 more
doaj   +1 more source

Embedding Stieltjes-Volterra integral equations in Stieltjes integral equations [PDF]

Transactions of the American Mathematical Society, 1977
J. A. Reneke has shown that the linear Stieltjes-Volterra integral equations studied by D. B. Hinton can be transformed into Stieltjes integral equations of the type studied by J. S. Mac Nerney. By taking advantage of the nonlinear nature of Mac Nerney’s results, Reneke was able to extend Hinton’s existence theorem to a nonlinear setting. In this paper,
openaire   +1 more source

Solving Bigeometric Volterra Integral Equations by Using Successive Approximations Method

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2021
In this study, the successive approximations method has been applied to investigate the solution for the linear bigeometric Volterra integral equations of the second kind in the sense of bigeometric calculus. The conditions to be taken into consideration
Nihan Güngör
doaj   +1 more source

A Practical Real‐Time Observer‐Based Radiation Prediction Algorithm for Solar Plants

Energy Science &Engineering, EarlyView.
A novel radiation prediction method is proposed. The model's existence is verified by applying real data to an offline identifier. An adaptive state/parameter estimator is developed to identify the model. The identification process occurs in real‐time, independent of specific situations. The method offers universal radiation prediction.
S. Sepehr Tabatabaei, S. Ayoub Mirtavousi, Mohammadreza Dehghan   +2 more
wiley   +1 more source

Convergence and data dependence results of the nonlinear Volterra integral equation by the Picard's three step iteration

AIMS Mathematics
Picard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature.
Lale Cona
doaj   +1 more source

Application of High‐Order Direct Flux Reconstruction and Stiffness‐Resilient Time Integration to Simulations of Idealized Atmospheric Flows

International Journal for Numerical Methods in Fluids, EarlyView.
The proposed work implements a direct flux reconstruction method for spatial discretization and a stiffness‐resilient exponential time integration method for temporal discretization on the cube‐sphere grid. A space‐time tensor formalism is employed to provide a general representation in any curvilinear coordinate system. This combination enables highly
Stéphane Gaudreault, Christopher Subich, Shoyon Panday, Martin Charron, Vincent Magnoux, Valentin Dallerit, Mayya Tokman   +6 more
wiley   +1 more source

Cordial Volterra Integral Equations and Singular Fractional Integro-Differential Equations in Spaces of Analytic Functions∗

Mathematical Modelling and Analysis, 2017
We study general cordial Volterra integral equations of the second kind and certain singular fractional integro-differential equation in spaces of analytic functions.
Urve Kangro
doaj   +1 more source

Some weakly singular Volterra integral inequalities with maxima in two variables

Journal of Inequalities and Applications, 2023
In this paper, we establish some new weakly singular Volterra type integral inequalities that include the maxima of the unknown function of two variables.
Yining Sun, Run Xu
doaj   +1 more source