| Summary: | Integral equations are extensively used in many physical models appearing in the field of plasma physics, atmosphere–ocean dynamics, fluid mechanics, mathematical physics and many other disciplines of physics and engineering. In this research work, a new numerical technique for the solution of the system of Fredholm integral equations (FIEs) of both first and second kinds is established, which is based on Bernstein basis functions. Here, the system of FIEs of both kinds has been taken, then reduces the equations to an algebraic linear system and can be solved using any standard rule. Convergence analysis of the proposed technique and some useful numerical results are presented so that the reader could understand this idea easily. Further, Hyers-Ulam stability analysis criteria is used for analyzing the stability of the proposed technique. The comparison of exact and approximate solutions of some problems is demonstrated in tables and their graphs are plotted to show the efficiency of the given technique.
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