This paper aims to developed a high-order and accurate method for the solution of one-dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order compact finite difference scheme for spatial part combined with implicit-explicit Runge Kutta scheme in temporal are proposed. Furthermore, boundary points are discretized by using a compact finite difference scheme in terms of fourth order accuracy. A key idea for proposed scheme is to take full advantage of method of line (MOL), this is consequently enabling us to use implicit-explicit Runge Kutta method, that are of fourth order in time. We constructed fourth order accuracy in both space and time and is unconditionally stable. This is consequently leading to a reduction in the computational cost of the scheme. Numerical experiments show that the combination of the compact finite difference with IMEX- RK methods give an accurate and reliable for solving the Lotka-Volterra-diffusion.

In this work, we study theA[α] – stability of the additive methods of Runge- Kutta kind of orders ranging from 2 up to 4 that will be applied for determining some stiff nonlinear system of the ODEs. Moreover, we find the stability function for the additive Runge-Kutta method and some methods of this type of order 2,3, and 4. Where the method (A,B₁) is A-stable and semi-implicit and method (A,B₂) is explicit. Furthermore, the stiff term is managed by the semi-implicit Runge-Kutta method while no stiff term is treated by the explicit Runge Kutta method. Those methods are suitable for solving chemical reactions problems that include stiff and non-stiff terms.

Digital information, especially multimedia and its applications, has grown exponentially in recent years. It is important to strengthen sophisticated encryption algorithms due to the security needs of these innovative systems. The security of real-time audio applications is ensured in the present study through a framework for encryption. The design framework protects the confidentiality and integrity of voice communications by encrypting audio applications. A modern method of securing communication and protecting data is cryptography. Using cryptography is one of the most important techniques for protecting data and ensuring the security of messaging. The main purpose of this paper is to present a novel encryption scheme that can be used in real-time audio applications. We encrypt the sound using a combination of an infinite series of hyperbolic functions and the Laplace transform, and then decrypt it using the inverse Laplace transform. The modular arithmetic rules are used to generate the key for the coefficients acquired from the transformation. There is no loss of data or noise in the decryption sound. We also put several sound examples to the test

Mathematical modeling and computer simulations aid global transmission parameter estimation. Equations, tools, and behavior assessments are vital in disease control modeling. The bacteria Vibrio cholera that causes the water-borne infectious disease cholera., which causes severe diarrhea and fast dehydration. Haiti exemplifies cholera's devastating impact. Despite its historical recognition, effective control plans are lacking. In this paper we review several paper choleras models. First, it can answer important questions about global health care and provide useful recommendations. After that, we examine the cholera model using sensitivity analyses with numerical simulation for all states. Full normalizations, half normalizations, and non-normalizations are used to evaluate the local sensitivities to each model states in relation to the model parameters. According to the sensitivity analysis, almost every model parameter might have an effect on the virus's spread among susceptible, and the most sensitive parameters are a and λ(B). So for preventing the spread of this disease with depending on the simulations the susceptible and infected people should be more careful about the parameters a (Rate of contact with polluted water) and λ(B). Finally, we intend to solve the Cholera disease using both the 5th order and 4th order ERK methods. Our aim is to then juxtapose our outcomes with those achieved through the conventional 4th order Runge-Kutta Method. This comparison will be facilitated by an assessment of their respective relative local truncation error estimators.

Many complex cell signalling pathways and chemical reaction networks include many variables and parameters; this is sometimes a big issue for identifying critical model elements and describing the model dynamics. Therefore, model reduction approaches can be employed as a mathematical tool to reduce the number of elements. In this study, we use a new technique for model reduction: the Lumping of parameters for the simple linear chemical reaction network and the complex cell signalling pathway that is extracellular-signal-regulated kinase (ERK) pathways. Moreover, we propose a high-order and accurate method for solving stiff nonlinear ordinary differential equations. The curtail idea of this scheme is based on splitting the problem into stiff and non-stiff terms. More specifically, stiff discretization uses the implicit method, and nonlinear discretization uses the explicit method. This is consequently leading to a reduction in the computational cost of the scheme. The main aim of this study is to reduce the complex cell signalling pathway models by proposing an accurate numerical approximation Runge-Kutta method. This improves one's understanding of such behaviour of these systems and gives an accurate approximate solution. Based on the suggested technique, the simple model's parameters are minimized from 6 to 3, and the complex models from 11 to 8. Results show that there is a good agreement between the original models and the simplified models.

The significance of image encryption has risen due to the widespread use of images as a key means of sharing data across different applications. Encryption methods are crucial in defending the confidentiality and integrity of valuable image data. This work proposes a novel method of image encryption technique based on the Elzaki transformation and substitution process, which is made possible by the extension of the Maclaurin series coefficients. The image is encrypted using an infinite series of hyperbolic functions and the Elzaki transform; the inverse Elzaki transform is then used to decrypt the image. Using modular arithmetic, the coefficients that result from the transformation are keyed.