On the Well-Posedness of a Class of Hybrid Weakly Singular Integro-Differential Equations

Numerical Methods for a Class of Hybrid Weakly Singular Integro-Differential Equations

This paper proposes numerical methods for solving hybrid weakly singular integro-differential equations of the second kind. The terms in these equations are in the following order: derivative term of a state, integro-differential term of a state with a weakly singular kernel, a state, integral term of a state with a smooth kernel, and force. The original class of weakly singular integro-differe...

Application of Tau Approach for Solving Integro-Differential Equations with a Weakly Singular Kernel

In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The  Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices....

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...

A note on a class of singular integro-differential equations

in which ak'S and bk'S are complex constants,fk(x) represents the kth derivative of the unknown function f(x) with prescribed initial valuesfk(0), along with the conditions thatfk(oo) = 0, for k = 0, 1, 2 . . . . . n, and 9(x) represents a known differentiable function arises in a natural way while solving a class of mixed boundary value problems of mathematical physics (see [-3, 5, 6]). Varley...

A Method to Estimate the Solution of a Weakly Singular Non-linear Integro-differential Equations by Applying the Homotopy Methods