Approximation of solutions to singular integro-differential equations by Hermite - Fejer polynomials

Numerical approximation based on the Bernouli polynomials for solving Volterra integro-differential equations of high order

In this ‎article‎‎, ‎an ‎ap‎plied matrix method, which is based on Bernouli Polynomials, has been presented to find approximate solutions of ‎high order ‎Volterra ‎integro-differential‎ equations. Through utilizing this approach, the proposed equations reduce to a system of algebric equations with unknown Bernouli coefficients. A number of numerical ‎illustrations‎ have been ‎solved‎ to ‎assert...

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...

Singular perturbations of integro-differential equations

We study the singular perturbation problem (E2) 2 2u′′ 2 (t) + u ′ 2(t) = Au2(t) + (K ∗Au2)(t) + f2(t), t ≥ 0, 2 > 0, for the integrodifferential equation (E) w′(t) = Aw(t) + (K ∗Aw)(t) + f(t), t ≥ 0, in a Banach space, when 2 → 0. Under the assumption that A is the generator of a strongly continuous cosine family and under some regularity conditions on the scalar-valued kernel K we show that p...

The Legendre Wavelet Method for Solving Singular Integro-differential Equations

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.

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