A matrix method for approximately solving certain linear and non-linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Chebyshev series approximation. The method is based on first taking the truncated Chebyshev series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear or non-linear system of algebraic equations with unknown Chebyshev coefficients. In addition, some equations considered by other authors are solved in terms of Chebyshev polynomials and the results are compared.

The cryptology is consisted of Kryptos (hidden) and logos (word) terms in the Greek. It also means that "secrecy science" at the communication. In the present days, the expansion of the electronic comminucation network has more increased the importance of cryptology. In this work, we have focused on Knapsack cryptosystem. In this purpose, the Bell numbers in the form of 'super-increasing sequence', which constitute the hypotenuse of the Bell triangle, are generated in the Python programming. The Knapsack encryption and decryption of these numbers are modeled using the Python program. As an example, "ULUDAG UNIVERSITY" was considered, a 12-bit encryption was performed. It was observed that the Bell numbers are suitable for Knapsack encryption.