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Mean Monte Carlo Finite Difference Method for Random Sampling of a Nonlinear Epidemic System
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In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained for each subpopulation as a vector distribution. The numerical outputs are tabulated, graphed, and compared with previous statistical estimations for 2013, 2015, and 2030, respectively. The solutions of FD and MMCFD are found to be in good agreement with small standard deviation of the means, and small measure of difference. The new MMCFD method is useful to predict intervals of random distributions for the numerical solutions of this epidemiology model with better approximation and agreement between existing statistical estimations and FD numerical solutions.

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Publication Date
Wed Feb 01 2023
Journal Name
Colloid Journal
Application of Hydrophilic Lipophilic Difference Theory for Fenofibrate Formulation as a Self-Emulsifying Drug Delivery System
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Improved oral bioavailability of lipophilic substances can be achieved using self-emulsifying drug delivery systems. However, because the properties of self-emulsifying are greatly influenced by surfactant amount and type, type of oil used, droplet size, charge, cosolvents, and physiological variables, the synthesis of self-emulsifying is highly complex; consequently, only a small number of excipient self-emulsifying formulations has been developed so far for clinical use. This study reports a highly effective procedure for developing self-emulsifying formulations using a novel approach based on the hydrophilic-lipophilic difference theory. Microemulsion characteristics, such as the constituents and amounts of oil and surfactant electrolyte

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Publication Date
Thu Feb 28 2019
Journal Name
Iraqi Journal Of Science
Approximation Solution of Nonlinear Parabolic Partial Differential Equation via Mixed Galerkin Finite Elements Method with the Crank-Nicolson Scheme
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The approximate solution of a nonlinear parabolic boundary value problem with variable coefficients (NLPBVPVC) is found by using mixed Galekin finite element method (GFEM) in space variable with Crank Nicolson (C-N) scheme in time variable. The problem is reduced to solve a Galerkin nonlinear algebraic system (NLAS), which is solved by applying the predictor and the corrector method (PCM), which transforms the NLAS into a Galerkin linear algebraic system (LAS). This LAS is solved once using the Cholesky technique (CHT) as it appears in the MATLAB package and once again using the General Cholesky Reduction Order Technique (GCHROT), the GCHROT is employed here at first time to play an important role for saving a massive time. Illustrative

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Publication Date
Mon Apr 26 2021
Journal Name
Journal Of Electrical Engineering & Technology
ANFIS Based Reinforcement Learning Strategy for Control A Nonlinear Coupled Tanks System
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Publication Date
Sun Sep 06 2015
Journal Name
Baghdad Science Journal
A New Three Step Iterative Method without Second Derivative for Solving Nonlinear Equations
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In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

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Publication Date
Sun Aug 01 2021
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Weighted Residual Method for the System of Nonlinear Volterra Integral Equations of the Second Kind Using an Exponential Function
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The numerical resolve nonlinear system of Volterra integral equation of the second kind (NLSVIEK2) has been considered. The exponential function is used as the base function of the collocation method to approximate the resolve of the problem. Arithmetic epitome are performed which have already been solved by weighted residual manner,  Taylor manner and block- by- block(2, 3, 5).

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
Building a Reliable Steganography System Using Random Key in a spatial Domain of Image
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With time progress importance of hiding information become more and more and all steganography applications is like computer games between hiding and extracting data, or like thieves and police men always thieve hides from police men in different ways to keep him out of prison. The sender always hides information in new way in order not to be understood by the attackers and only the authorized receiver can open the hiding message. This paper explores our proposed random method in detail, how chooses locations of pixel in randomly , how to choose a random bit to hide information in the chosen pixel, how it different from other approaches, how applying information hiding criteria on the proposed project, and attempts to test out in code, and

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Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
Runge-kutta Numerical Method for Solving Nonlinear Influenza Model
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Abstract<p>The main object of this study is to solve a system of nonlinear ordinary differential equations (ODE) of the first order governing the epidemic model using numerical methods. The application under study is a mathematical epidemic model which is the influenza model at Australia in 1919. Runge-kutta methods of order 4 and of order 45 for solving this initial value problem(IVP) problem have been used. Finally, the results obtained have been discussed tabularly and graphically.</p>
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Publication Date
Tue Apr 20 2021
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Sumudu Iterative Method for solving Nonlinear Partial Differential Equations
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       In this paper, we apply a new technique combined by a Sumudu transform and iterative method called the Sumudu iterative method for resolving non-linear partial differential equations to compute analytic solutions. The aim of this paper is to construct the efficacious frequent relation to resolve these problems. The suggested technique is tested on four problems. So the results of this study are debated to show how useful this method is in terms of being a powerful, accurate and fast tool with a little effort compared to other iterative methods.

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Publication Date
Fri Nov 01 2013
Journal Name
Al-nahrain Journal Of Science
Modified third order iterative method for solving nonlinear equations
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Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

Publication Date
Sun Mar 01 2009
Journal Name
Diyala Journal Of Human Research
Stability of the Finite Difference Methods of Fractional Partial Differential Equations Using Fourier Series Approach
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The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

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