Integral equations are widely used in many physical models appearing in the fields of plasma physics, atmospheric-ocean dynamics, fluid mechanics, mathematical physics, and many other branches of physics. and science and technology. In this work, a new digital technique for solving systems of Fredholm Integral Equations (FIEs) of the first and second types is established, based on Bernstein basis functions. Here, the FIE system of both types has been taken and then reduced to an algebraic linear system that can be solved using any of the standard rules. Convergence analysis of the proposed technique and some useful numerical results are presented so that the reader can easily understand the idea. In addition, the HyersUlam stability analysis criterion was used to analyze the stability of the proposed technique.
