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In this paper, a new 4D chaos system is introduced based on the mathematical structure through composing and transferring. The behavior of the proposed chaotic system is studied using different tests, such as Lyapunov exponent, bifurcation diagram and histogram. In order to show the advantage of the new chaos system, the proposed system is used for image encryption. In the proposed algorithm, in addition to the new chaos system, cellular automata is also used to improve the security of the algorithm. The proposed algorithm has a separate structure for encryption key, which increases the security of the proposed algorithm. The security of the proposed environment which is evaluated using different types of security tests shows the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this work, collocation method based on B-spline functions is used to obtained a numerical solution for one-dimensional hyperbolic telegraph equation. The proposed method is consists of two main steps. As first step, by using finite difference scheme for time variable, partial differential equation is converted to an ordinary differential equation by space variable. In the next step, for solving this equation collocation method is used. In the analysis section of the proposed method, the convergence of the method is studied. Also, some numerical results are given to demonstrate the validity and applicability of the presented technique. The L∞, L2 and Root-MeanSquare(RMS) in the solutions show the efficiency of the method computationally. [ABSTRACT FROM AUTHOR]

In this paper we study the deviation of the error estimation for the second order Fredholm-Volterra integro-differential equations. We prove that formdegree piecewise polynomial collocation method, our method providesO(hm+1) as the order of the deviation of the error. Also numerical results in the final section are included to confirm the theoretical results. [ABSTRACT FROM PUBLISHER]