In this paper, a useful matrix approach for high-order linear Fredholm integro-differential equations with initial boundary conditions expressed as Lucas polynomials is proposed. Using a matrix equationwhich is equivalent to a set of linear algebraic equations the method transforms to integro-differential equation. When compared to other methods that have been proposed in the literature, the numerical results from the suggested technique reveal that it is effective and promising. And also, error estimation of the scheme was derived. These results were compared with the exact solutions and the other numerical methods to the tested problems.

Keywords:
## Fredholm integro-differential equations, Initial value problem Lucas matrix method, Lucas polynomials and series,

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**Başlangıç:**2018**Yayıncı:**International Society of Academicians

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