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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
Wed May 13 2020
Journal Name
Nonlinear Engineering
Two meshless methods for solving nonlinear ordinary differential equations in engineering and applied sciences
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Abstract<p>In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using <italic>Mathematica</italic>® 10. Four applications, which are the well-known nonlinear problems: the magnetohydrodynamic squeezing fluid, the Jeffery-Hamel flow, the straight fin problem and the Falkner-Skan equation are presented and solved using the proposed methods. To ill</p> ... Show More
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Publication Date
Sun Sep 01 2024
Journal Name
Partial Differential Equations In Applied Mathematics
Perturbation iteration transform method for solving fractional order integro-differential equation
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Publication Date
Sun Jun 07 2015
Journal Name
Baghdad Science Journal
Direct method for Solving Nonlinear Variational Problems by Using Hermite Wavelets
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In this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.

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Publication Date
Thu Mar 06 2025
Journal Name
Aip Conference Proceedings
Solving 5th order nonlinear 4D-PDEs using efficient design of neural network
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Publication Date
Sat Nov 01 2014
Journal Name
International Journal Of Basic And Applied Sciences
A reliable iterative method for solving the epidemic model and the prey and predator problems
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In the present article, we implement the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763] to solve two problems; the first one is the problem of spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of the prey and predator. The results demonstrate that the method has many merits such as being derivative-free, overcome the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition Method (ADM), does not require to calculate Lagrange multiplier a

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Publication Date
Thu Jan 01 2015
Journal Name
Journal Of The College Of Basic Education
Efficient Modifications of the Adomian Decomposition Method for Thirteenth Order Ordinary Differential Equations
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This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

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Publication Date
Mon Aug 01 2022
Journal Name
Baghdad Science Journal
Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems
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This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

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Publication Date
Sun Jun 23 2019
Journal Name
Journal Of The College Of Basic Education
Numerical Solution of Non-linear Delay Differential Equations Using Semi Analytic Iterative Method
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Publication Date
Fri Jun 23 2023
Journal Name
Journal The College Of Basic Education / Al-mustansiriyah University
Numerical Solution of Non-linear Delay Differential Equations Using Semi Analytic Iterative Method
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We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

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Publication Date
Sun Jun 07 2015
Journal Name
Baghdad Science Journal
A Solution of Second Kind Volterra Integral Equations Using Third Order Non-Polynomial Spline Function
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In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.

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