Approximati of solutions of 2d non-linear integral equations in a binary hilbert space

In this work, we investigate stability of solutions relative to the driver to a general class of nonlinear integral equations in two dimensions in binary reproducing kernel Hilbert space. Next, we analyze estimate error of solutions in terms of uniform grid numbers of compact subintervals of [a, b] × [c, d]. In addition, we use the reproducing kernel method to approximate the solutions of the problem. Finally, we provide an example to illustration the reliability of the method