Results 81 to 90 of about 2,862 (195)

Initial-boundary value problems for integrable evolution equations with $3 \times 3$ Lax pairs

, 2012
We present an approach for analyzing initial-boundary value problems for integrable equations whose Lax pairs involve $3 \times 3$ matrices. Whereas initial value problems for integrable equations can be analyzed by means of the classical Inverse ...
Lenells, Jonatan
core   +1 more source

A Projection Method for Solving Nonlinear Volterra-Fredholm Integral Equations using Legendre Hybrid Functions

Journal of Mathematical Extension, 2013
Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them.
M. Roodaki, Z. JafariBehbahani
doaj  

The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1

, 2004
An analog of Gelfand-Levitan-Marchenko integral equations for multi- dimensional Delsarte transmutation operators is constructed by means of studying their differential-geometric structure based on the classical Lagrange identity for a formally ...
Chern S.S., Danford N., De Rham G., Godbillon C., Teleman R., Warner F.   +5 more
core   +2 more sources

Numerical solution of special 2D Fredholm-Volterra integral equations using barycentric Gegenbauer interpolation collocation method

Journal of Physics: Conference Series, 2020
Abstract In this paper, an efficient collocation method based on two dimensional barycentric Gegenbauer interpolation is used to solve a kind of special two dimensional Fredholm-Volterra integral equations (2D-FVIEs). The explicit barycentric weights for the Gegenbauer-Gauss nodes not only reduce the complicated calculation but also ...
Hongyan Liu, Jin Huang
openaire   +1 more source

Solvability of Implicit Fractional Systems With Nonlocal Conditions in Weighted Functional Spaces

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
This paper investigates the existence and uniqueness of solutions for a class of nonlinear implicit Riemann–Liouville fractional integro‐differential equations subject to nonlocal conditions in a weighted Banach space. The inclusion of both implicit effects and nonlocal terms introduces additional complexity, making the analysis both challenging and ...
Abdulrahman A. Sharif, Maha M. Hamood, Kirtiwant P. Ghadle, Sining Zheng   +3 more
wiley   +1 more source

Hybrid functions approach to solve a class of Fredholm and Volterra integro-differential equations

, 2019
In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations.
Bhalekar, Sachin, Hosry, Aline, Nakad, Roger   +2 more
core   +1 more source

Approximate Solution of Intuitionistic Fuzzy Volterra Integral Equation of Separable‐Type Kernel Using Elzaki Adomian Decomposition Method

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
An intuitionistic fuzzy number, which incorporates both membership and nonmembership functions at a same time, allows for a more accurate representation of uncertainty. This work presents an approximate solution to the Volterra integral equation that involves both membership and nonmembership degrees of uncertainty named as intuitionistic fuzzy ...
Zain Khan, Saleem Abdullah, Samuel Okyere, Bikash Koli Dey   +3 more
wiley   +1 more source

An accelerated iterative technique for solving mixed Fredholm-Volterra integral equations

Ain Shams Engineering Journal
In this paper, we propose an accelerated numerical technique for solving mixed Fredholm-Volterra integral equations (MFVIEs). The MFVIE is solved using the two-grid iterative technique, which uses a small system of equations to reach higher accuracy. The convergence analysis showed that using this technique reduces computational costs by 85% compared ...
A.G. Attia, I.L. El-kalla, A. Elsaid, R.A. Abd El-Monem   +3 more
openaire   +2 more sources

An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This article extends a spectral collocation approach based on Lucas polynomials to numerically solve the integrodifferential equations of both Volterra and Fredholm types for multi–higher fractional order in the Caputo sense under the mixed conditions. The new approach focusses on using a matrix strategy to convert the supplied equation with conditions
Shabaz Jalil Mohammedfaeq, Miran Bayan Mohammed Amin, Dashne Chapuk Zahir, Shazad Shawki Ahmed, Saeid Abbasbandy   +4 more
wiley   +1 more source

A Product Integration type Method for solving Nonlinear Integral Equations in L

, 2016
This paper deals with nonlinear Fredholm integral equations of the second kind. We study the case of a weakly singular kernel and we set the problem in the space L 1 ([a, b], C). As numerical method, we extend the product integration scheme from C 0 ([a,
Ahues, M., Grammont, L., Kaboul, H.
core   +5 more sources