In this paper, we presented three mathematical models to calculate the amount of radon concentration in water which is considered a poisonous gas. two of these models are established by numerical methods, which are the Neville method and the Spline method. The graph approach is used to create the third model. It is notable that the current study is original and having a novelty as it has created for the first time three mathematical methods to calculate radon gas concentrations in water; as well as it is the first study that has applied the numerical methods to carry out the calculations. the results obtained from these methods are compared with previous studies and then finding the error rates. After that, we have made a comparison between these three models to obtain the best one. Since the error rate is slightly lower than the Neville method so the Spline method is the best of the three methods that we worked with.
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
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