In this paper, the linear barycentric rational interpolation collocation method for solving one‐ and two‐dimensional telegraph equation is presented. The barycentric rational interpolation is introduced. Following the barycentric rational interpolation method, the matrix form of the collocation method is also obtained which can be easily programmed. With the help of the convergence rate of the linear barycentric rational interpolation, the convergence rate of linear barycentric rational collocation method for solving telegraph equation is proved. At last, several numerical examples are provided to show the convergence rate and verify the correctness of the theoretical analysis.

<abstract><p>Image encryption has been an important research topic in information security. Different from traditional encryption methods, heat flow cryptosystem is a new encryption method. This paper proposes an image encryption algorithm based on heat flow cryptosystem. First, a class of heat flow cryptosystem based on nonlinear pseudo-parabolic equations are given in this paper. Second, a numerical method with high precision namely barycentric Lagrange interpolation collocation method is proposed to solve the nonlinear pseudo-parabolic equation. Third, an image encryption algorithm based on the heat flow cryptosystem is designed, the detailed process of encryption and decryption algorithm is given, the flow diagram of algorithm is showed. Finally, the proposed encryption algorithm is applied to various image with gray and RGB format and compared with the current popular chaotic encryption algorithm. Many indicators such as histograms, information entropy and correlation are used to objectively evaluate the image encryption algorithm. The experimental results show that the proposed image encryption algorithm is better in most indicators and the algorithm is sensitive to the change of key and plaintext.</p></abstract>

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