A Nystrom Method for 2D Fredholm-Hammerstein Integral Equations Defined on a Square
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Integral equations model a variety of applied problems, for example in mechanics, chemistry, electronics engineering, computer graphics and so on. Moreover some differential problems, tipically BVP type, can be reformulated in terms of integral equations. The nonlinear case is particularly interesting and add difficulties to the numerical approximation of such equations. The topic of the talk is the numerical approximation of 2D nonlinear integral equations of Fredholm--Hammerstein type, defined on the closed square [-1,1]X[-1,1]. Recently some numerical methods about the 2D nonlinear integral equations defined on a rectangle appeared in the literature. Here we propose a global approximation approach, consisting in a numerical method of Nystrom type based on a Gaussian tensorial cubature formula. The global approximation approach is very competitive w.r.t. the other known methods. The proposed method is proved to be stable and convergent. Moreover it is shown that the Nystrom interpolant behaves like the best polynomial approximation of the solution in the space of continuous functions.