scholarly journals Modified Homotopy Perturbation Technique for the Approximate Solution of Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Farooq Ahmed Shah
Keyword(s):  
Approximate Solution ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Perturbation Technique ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
New Methods ◽  
And Performance ◽  
Homotopy Perturbation Technique

We use a new modified homotopy perturbation method to suggest and analyze some new iterative methods for solving nonlinear equations. This new modification of the homotopy method is quite flexible. Various numerical examples are given to illustrate the efficiency and performance of the new methods. These new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations.

scholarly journals Some New Iterative Methods for Nonlinear Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Eisa Al-Said ◽  
Muhammad Waseem
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
System Of Equations ◽  
Decomposition Technique ◽  
Methods Comparison ◽  
Numerical Examples ◽  
New Methods ◽  
And Performance

We suggest and analyze some new iterative methods for solving the nonlinear equationsf(x)=0using the decomposition technique coupled with the system of equations. We prove that new methods have convergence of fourth order. Several numerical examples are given to illustrate the efficiency and performance of the new methods. Comparison with other similar methods is given.

Extended conjugate gradient squared and conjugate residual squared methods for solving the generalized coupled Sylvester tensor equations

2020 ◽  
pp. 014233122093238
Author(s):  
Eisa Khosravi Dehdezi ◽  
Saeed Karimi
Keyword(s):  
Iterative Methods ◽  
Conjugate Gradient ◽  
Numerical Examples ◽  
New Methods ◽  
Conjugate Gradient Squared ◽  
And Performance ◽  
Tensor Computations ◽  
Conjugate Residual

In this paper, two attractive iterative methods – conjugate gradient squared (CGS) and conjugate residual squared (CRS) – are extended to solve the generalized coupled Sylvester tensor equations [Formula: see text]. The proposed methods use tensor computations with no maricizations involved. Also, some properties of the new methods are presented. Finally, several numerical examples are given to compare the efficiency and performance of the proposed methods with some existing algorithms.

scholarly journals A Family of Fourteenth-Order Convergent Iterative Methods for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fiza Zafar ◽  
Gulshan Bibi
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
Numerical Examples ◽  
New Class ◽  
First Derivative ◽  
New Methods ◽  
Specific Step

We present a family of fourteenth-order convergent iterative methods for solving nonlinear equations involving a specific step which when combined with any two-step iterative method raises the convergence order by n+10, if n is the order of convergence of the two-step iterative method. This new class include four evaluations of function and one evaluation of the first derivative per iteration. Therefore, the efficiency index of this family is 141/5 =1.695218203. Several numerical examples are given to show that the new methods of this family are comparable with the existing methods.

scholarly journals Approximate Solution of Nonlinear Integral Equations of the Second Kind by Using Homotopy Perturbation Method

2017 ◽  
Vol 65 (2) ◽  
pp. 151-155
Author(s):  
MM Hasan ◽  
MA Matin
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Perturbation Method ◽  
Fredholm Integral Equation ◽  
Homotopy Perturbation Method ◽  
Nonlinear Integral Equations ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Nonlinear Fredholm Integral Equation

In this paper, we apply Homotopy perturbation method (HPM) for obtaining approximate solution of nonlinear Fredholm integral equation of the second kind. Finally, some numerical examples are provided, and the obtained numerical approximations are compared with the corresponding exact solution. Dhaka Univ. J. Sci. 65(2): 151-155, 2017 (July)

SOME HIGH ORDER ITERATIVE METHODS FOR NONLINEAR EQUATIONS BASED ON THE MODIFIED HOMOTOPY PERTURBATION METHODS

2010 ◽  
Vol 03 (03) ◽  
pp. 395-408
Author(s):  
Bilian Chen ◽  
Yajun Xie ◽  
Changfeng Ma
Keyword(s):  
Nonlinear Equation ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Perturbation Methods ◽  
Systems Of Nonlinear Equations ◽  
Convergence Criteria ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Nonlinear Equation Systems ◽  
High Order Iterative Methods

In this paper, we present some efficient iterative methods for solving nonlinear equation (systems of nonlinear equations, respectively) by using modified homotopy perturbation methods. We also discuss the convergence criteria of the present methods. Some numerical examples are given to illustrate the performance and efficiency of the proposed methods.

scholarly journals Novel Three Order Methods for Solving a System of Nonlinear Equations

2012 ◽  
Vol 2 ◽  
pp. 1-12 ◽  
Author(s):  
M.Q. Khirallah ◽  
M.A. Hafiz
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Newton Method ◽  
System Of Nonlinear Equations ◽  
Numerical Examples ◽  
And Performance ◽  
Predictor Corrector ◽  
New Algorithms

In this paper, we suggest and study Simpson's formula, and Newton's two, three and four Cosed formulas iterative methods for solving the system of nonlinear equations by using Predictor-Corrector of Newton method. We present four new algorithms for solving the system of nonlinear equations (SNLE). We prove that these new algorithms have convergence. Several numerical examples are given to illustrate the efficiency and performance of the new iterative methods. These new algorithms may be viewed as an extensions and generalizations of the existing methods for solving the system of nonlinear equations.

Based on the Improved Homotopy Perturbation Method for Solving Nonlinear Equations

2013 ◽  
Vol 275-277 ◽  
pp. 836-840
Author(s):  
Xi Qin He ◽  
Hai Yang Li
Keyword(s):  
Integral Equation ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

According to Nonlinear Fredholm differential and integral equation，it is proposed that the improved homotopy perturbation method is used to solve in this paper, and apply the numerical examples to compare the advantages among homotopy perturbation method, Adomian decomposition method and improved homotopy perturbation method . The results show that improved homotopy perturbation method is more effective.

scholarly journals Application of the Laplace Homotopy Perturbation Method to the Black–Scholes Model Based on a European Put Option with Two Assets

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 310 ◽  
Author(s):  
Din Prathumwan ◽  
Kamonchat Trachoo
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Explicit Solution ◽  
Homotopy Perturbation Method ◽  
Approximation Methods ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Put Option ◽  
Black Scholes Model ◽  
Black Scholes

In this paper, the Laplace homotopy perturbation method (LHPM) is applied to obtain the approximate solution of Black–Scholes partial differential equations for a European put option with two assets. Different from all other approximation methods, LHPM provides a simple way to get the explicit solution which is represented in the form of a Mellin–Ross function. The numerical examples represent that the solution from the proposed method is easy and effective.

scholarly journals Decomposition Technique and a Family of Efficient Schemes for Nonlinear Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Farooq Ahmed Shah ◽  
Maslina Darus ◽  
Imran Faisal ◽  
Muhammad Arsalan Shafiq
Keyword(s):  
Applied Sciences ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Decomposition Technique ◽  
Unified Framework ◽  
New Methods ◽  
New Family ◽  
And Performance

Various problems of pure and applied sciences can be studied in the unified framework of nonlinear equations. In this paper, a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique. The convergence of the new methods is proven. For the implementation and performance of the new methods, some examples are solved and the results are compared with some existing methods.

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