Results 111 to 120 of about 13,396 (146)

Numerical solutions of Abel integral equations via Touchard and Laguerre polynomials

2021
In this article, two numerical methods based on Touchard and Laguerre polynomials were presented to solve Abel integral (AI) equations. Touchard and Laguerre matrices were utilized to transform Abel integral equations into an algebraic system of linear equations. Solve this system of these equations to obtain Touchard and Laguerre parameters.
Talab Abdullah, Jalil, Sweedan Naseer, Bushra, Taha Abdllrazak, Balasim   +2 more
openaire   +1 more source

New fractional Lanczos vector polynomials and their application to system of Abel–Volterra integral equations and fractional differential equations

Journal of Computational and Applied Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D. Conte, S. Shahmorad, Y. Talaei
openaire   +3 more sources

Numerical solution of Abel equation using operational matrix method with Chebyshev polynomials

Asian-European Journal of Mathematics, 2017
In this paper, we present a numerical scheme for solving the Abel equation. The approach is based on the shifted Chebyshev polynomials together with operational method. We reduce the problem to a set of nonlinear algebraic equations using operational matrix method. In addition, convergence analysis of the method is presented.
Öztürk, Yalçın, Gülsu, Mustafa
openaire   +2 more sources

A novel numerical approach based on shifted second‐kind Chebyshev polynomials for solving stochastic Itô–Volterra integral equation of Abel type with weakly singular kernel

Mathematical Methods in the Applied Sciences, 2023
In this paper, a collocation method based on shifted second‐order Chebyshev polynomials is implemented to obtain the approximate solution of the stochastic Itô–Volterra integral equation of Abel type with weakly singular kernel. In this method, operational matrices are used to convert the stochastic Itô–Volterra integral equation to algebraic equations
Santanu Saha Ray, Reema Gupta
openaire   +1 more source

An efficient solution of system of generalized Abel integral equations using Bernstein polynomials wavelet bases

Mathematical Sciences, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shweta Pandey, Sandeep Dixit, S. R. Verma   +2 more
openaire   +2 more sources

Generalized centre conditions and multiplicities for polynomial Abel equations of small degrees

Nonlinearity, 1999
Summary: We consider the Abel equation \((*)\;y'=p(x)y^2+q(x)y^3\) with \(p(x),q(x)\) polynomials in \(x\). A centre condition for this equation (closely related to the classical centre condition for polynomial vector fields on the plane) is that \(y_0=(0)\equiv y(1)\) for any solution \(y(x)\).
Blinov, M., Yomdin, Y.
openaire   +1 more source

B-polynomial multiwavelets approach for the solution of Abel's integral equation

International Journal of Computer Mathematics, 2010
A numerical method for solving Abel's integral equation as singular Volterra integral equations is presented. The method is based upon Bernstein polynomial (B-polynomial) multiwavelet basis approximations. The properties of B-polynomial multiwavelets are first presented.
openaire   +1 more source

Orthonormal Bernoulli polynomials collocation approach for solving stochastic Itô‐Volterra integral equations of Abel type

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2019
AbstractIn this paper, orthonormal Bernoulli collocation method has been developed to obtain the approximate solution of linear singular stochastic Itô‐Volterra integral equations. By applying this method, linear stochastic integral equation converts to linear system of algebraic equations. This system is achieved by approximating functions that appear
Nasrin Samadyar, Farshid Mirzaee
openaire   +1 more source

Stable inversion of the Abel integral equation of the first kind by means of orthogonal polynomials

Inverse Problems, 2010
In this paper, we describe two stable methods for the inversion of the Abel integral operator of the first kind. The first method is based on the use of appropriate families of orthonormal polynomials of Jacobi type that constitute orthonormal bases of the L2([0, 1])-space.
Amara Ammari, Abderrazek Karoui
openaire   +1 more source

On the solution of the Abel equation of the second kind by the shifted Chebyshev polynomials

Applied Mathematics and Computation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gülsu, Mustafa, Öztürk, Yalçın, Sezer, Mehmet   +2 more
openaire   +1 more source