This article presents a computational method for solving a problem with parameter for a system of Fredholm integro-differential equations. Some additional parameters are introduced and the problem under consideration is reduced to solving a system of linear algebraic equations. The coefficients and right-hand side of the system are calculated by solving the Cauchy problems for ordinary differential equations. We establish a criterion for the unique solvability of the problem under consideration. A numerical algorithm is offered for solving the problem with parameter. The results are illustrated by numerical examples. Keywords Problem with parameter • System of integro-differential equations • Solvability criteria • Algorithm • Computational method Mathematics Subject Classification 34B08 • 34H05 • 45J05 • 34K28 Communicated by Antonio José Silva Neto.

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