JOURNAL OF ADVANCES IN MATHEMATICS 2024-02-02T12:36:18+00:00 Editorial Office Open Journal Systems Application Of Multipoint Secant-Type Method ForFinding Roots 0f Nonlinear Equations 2024-02-02T12:36:18+00:00 R. Thukral <p><span style="font-weight: 400;">In this paper, we introduce a family of </span><span style="font-weight: 400;">p</span><sub><span style="font-weight: 400;">k</span></sub><span style="font-weight: 400;">-order iterative schemes for finding the simple root of a nonlinear algebraic equation of the function </span><span style="font-weight: 400;">f</span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">=0</span><span style="font-weight: 400;"> by using the divided difference approximation. The proposed method uses one evaluation of the function per iteration and can achieve convergence order </span><span style="font-weight: 400;">p</span><sub><span style="font-weight: 400;">k</span></sub><span style="font-weight: 400;">. The error equation and asymptotic convergence constant are proved theoretically and numerically. Numerical examples are included to demonstrate the exceptional convergence speed of the proposed method and thus verify the theoretical results</span></p> 2024-02-22T00:00:00+00:00 Copyright (c) 2024 R. Thukral Proposed Development of NTRU Public Key Encryption 2024-01-23T19:45:47+00:00 Marwah Aearaby Sayyid <p>The 1996 proposal by Hoffstein, Pfeiffer, and Silverman for the NTRU public key encryption system provides a quick and useful substitute for factorization- or discrete logarithm-based classical programs. It rovides approximate security against quantum computing assaults and earoptimal asymptotic efficiency, in contrast to these latter approaches. The security analysis of the system involves examining naturally occurring computational and statistical challenges that are defined on finite polynomial rings. Current advancements in the broader field of latticebased cryptography, include security studies and applications of NTRU and its variations. These advancements include the creation of multilinear.</p> 2024-01-29T00:00:00+00:00 Copyright (c) 2024 MARWAH AEARABY SAYYID Using The Box-Jenkins Method In Time Series To Predict The Monthly Electrical Loads In (Babylon Governorate - Shomali District) 2024-01-05T13:03:18+00:00 Hayder Kadim Mohammed Ali Kazim Jari Wissam Sadiq Khudair <p><span style="font-weight: 400;">The topic of time series analysis is considered one of the important statistical topics to explain the phenomena that occur during a specific period of time. Time sequence examination objects to find an accurate account of the sequence, build a suitable perfect to interpret its behavior, and use the effects to predict the future time series . We using the Box-Jenkins method in the period sequence to predict the monthly electrical loads in (Babylon Governorate - Shomali district), and we have found that the studied time series is unstable in the mean and variance, we note that the time series is stable in the nasty and alteration. Autocorrelation and incomplete autocorrelation coefficients are used for the original data. Through these coefficients, we conclude that the appropriate model for the data is (3-1-2) ARMA. This model was chosen as it obtained the least (ARAM), and thus the model is appropriate for the data and the use of predictive values until the year (2022).</span></p> 2024-01-29T00:00:00+00:00 Copyright (c) 2024 Hayder Kadim Mohammed, Ali Kazim Jari, Wissam Sadiq Khudair An Engineering Boundary Eigenvalue Problem Studied by Functional-Analytic Methods 2024-01-02T09:18:47+00:00 L. Kohaupt <p>In this paper, we take up a boundary value problem (BVP) from the area of engineering that is described in a book by L. Collatz. Whereas there, the BVP is cast into a boundary eigenvalue problem (BEVP) having complex eigenvalues, here the original BVP is transformed into a BEVP that has positive simple eigenvalues and real eigenfunctions. Further, unlike there, we derive the inverse T = G of the differential operator L associated with the BEVP, show that T = G is compact in an appropriate real Hilbert space H, expand T u = Gu and u for all u ∈ H in a respective series of eigenvectors, and obtain max-, min-, min-max, and max-min-Rayleigh-quotient representation formulas of the eigenvalues. Specific examples for generalized Rayleigh quotients illustrate the theoretical findings. The style of the paper is expository in order to address a large readership.</p> 2024-01-29T00:00:00+00:00 Copyright (c) 2024 L. Kohaupt Couple New Iterative Method with Pade Approximation to Solve the Nonlinear Wave-Like Equations with Variable Coefficients 2023-12-10T11:26:14+00:00 Rana T. Shwayyea <p><span style="font-weight: 400;">In this paper, some cases of wave-like equation have been solved by modified new iterative method as an infinite power series but it is impossible to compute the infinite series, therefore, the truncated power series was approximated by Pade approximation. Pade approximation approximates a truncated power series as ratio of two polynomials to reduce calculations and shorten the power series while maintaining accuracy. These cases are shown the successful use of solution approximation by Pade approximation compared to power series expansion.</span></p> 2024-01-24T00:00:00+00:00 Copyright (c) 2024 Rana T. Shwayyea