The Experts below are selected from a list of 18252 Experts worldwide ranked by ideXlab platform

Muhammad Aslam Noor - One of the best experts on this subject based on the ideXlab platform.

  • Derivative-Free Iterative Methods for Solving Nonlinear Equations
    Applied Mathematics & Information Sciences, 2014
    Co-Authors: Farooq Ahmed Shah, Muhammad Aslam Noor, Moneeza Batool
    Abstract:

    In this paper, we suggest and analyze some new derivative free iterative methods for Solving Nonlinear Equation f (x) = 0 using a suitable transformation. We also give several examples to illustrate the efficiency of these methods. Comparison with other similar method is also given. These new methods can be considered as alternative to the developed methods. This technique can be used to suggest a wide class of new iterative methods for Solving Nonlinear Equations.

  • new iterative methods for Solving Nonlinear Equation by using homotopy perturbation method
    Applied Mathematics and Computation, 2012
    Co-Authors: Muhammad Aslam Noor, Waseem Asghar Khan
    Abstract:

    In this paper, we suggest and analyze a new class of iterative methods for Solving Nonlinear Equations by using the homotopy perturbation method. Convergence of their method is also considered. Here we also discuss the efficiency index and computational order of convergence of new methods. Several numerical examples are given to illustrate the efficiency and performance of these new methods. These new iterative methods may be viewed as an extension and generalization of the existing methods for Solving Nonlinear Equations.

  • Fifth-order iterative methods for Solving Nonlinear Equations
    Applied Mathematics and Computation, 2007
    Co-Authors: Muhammad Aslam Noor, Khalida Inayat Noor
    Abstract:

    Abstract In this paper, we suggest and analyze a new two-step iterative method for Solving Nonlinear Equation f ( x ) = 0 by rewriting the given Nonlinear Equation as a coupled system of Equations and using the Taylor series. It is shown that this new iterative method is of fifth-order. Several examples are given to illustrate its performance and efficiency. Comparison with other methods is also given. This method can be viewed as an improvement of the Halley’s method.

  • On iterative methods for Nonlinear Equations
    Applied Mathematics and Computation, 2006
    Co-Authors: Muhammad Aslam Noor, Waseem Asghar Khan, Khalida Inayat Noor, Faizan Ahmad
    Abstract:

    Several iterative methods have been suggested and analyzed for Solving Nonlinear Equation f(x)=0. All these methods can be classified as one-step and two-step methods. In this paper, we have suggested and analyzed several two-step methods for Solving Nonlinear Equations. We have also shown that these two-step methods are quadratically convergent. Several numerical examples are given to illustrate this comparison. Our results can be viewed as important refinement and improvement of the previously known results.

Jun Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Solving Nonlinear Equation systems using multiobjective differential evolution
    International Conference on Evolutionary Multi-criterion Optimization, 2019
    Co-Authors: Jun Zhang
    Abstract:

    Nonlinear Equation systems (NESs) usually have more than one optimal solution. However, locating all the optimal solutions in a single run, is one of the most challenging issues for evolutionary optimization. In this paper, we address this issue by transforming all the optimal solutions of an NES to the nondominated solutions of a constructed multiobjective optimization problem (MOP). In the general case, we prove that the proposed transformation fully matches the requirement of multiobjective optimization. That is, the multiple objectives always conflict with each other. In this way, multiobjective optimization techniques can be used to locate these multiple optimal solutions simultaneously as they locate the nondominated solutions of the MOPs. Our proposed approach is evaluated on 22 NESs with different features, such as linear and Nonlinear Equations, different numbers of optimal solutions, and infinite optimal solutions. Experimental results reveal that the proposed approach is highly competitive with some other state-of-the-art algorithms for NES.

  • EMO - Solving Nonlinear Equation Systems Using Multiobjective Differential Evolution
    Lecture Notes in Computer Science, 2019
    Co-Authors: Jun Zhang
    Abstract:

    Nonlinear Equation systems (NESs) usually have more than one optimal solution. However, locating all the optimal solutions in a single run, is one of the most challenging issues for evolutionary optimization. In this paper, we address this issue by transforming all the optimal solutions of an NES to the nondominated solutions of a constructed multiobjective optimization problem (MOP). In the general case, we prove that the proposed transformation fully matches the requirement of multiobjective optimization. That is, the multiple objectives always conflict with each other. In this way, multiobjective optimization techniques can be used to locate these multiple optimal solutions simultaneously as they locate the nondominated solutions of the MOPs. Our proposed approach is evaluated on 22 NESs with different features, such as linear and Nonlinear Equations, different numbers of optimal solutions, and infinite optimal solutions. Experimental results reveal that the proposed approach is highly competitive with some other state-of-the-art algorithms for NES.

Rahim Shoghi - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear dynamic analysis of tlp surge motion using homotopy perturbation method
    Ships and Offshore Structures, 2014
    Co-Authors: Mohammad Reza Tabeshpour, Rahim Shoghi
    Abstract:

    Tension leg platforms (TLPs) are well-known structures for oil exploitation in deep water. One of the current issues in compliant structures in the sea is variation in frequency and structural response due to a Nonlinear parameter in the Equation of motion. Variation of frequency is important in fatigue life study of tethers. A perturbation method is used in contrast to the traditional methods. This method does not require a small parameter for finding surge motion of TLP. In this paper, homotopy perturbation method (HPM) is used to solve a highly Nonlinear differential Equation of surge motion. Calculated responses by HPM are compared with those obtained from both linear and Nonlinear Equations of motion. Numerical method is used for Solving Nonlinear Equation of motion and ordinary differential method is used for linear Equation of motion. It is very useful for a design engineer to have a deep view of Nonlinear vibration behaviour of systems which are naturally Nonlinear like TLP.

  • comparison between linear and Nonlinear models for surge motion of tlp
    The international journal of marine science, 2012
    Co-Authors: Mohammad Reza Tabeshpour, Rahim Shoghi
    Abstract:

    Tension-Leg Platform (TLP) is a vertically moored floating structure. The platform is permanently moored by tendons. Surge Equation of motion of TLP is highly Nonlinear because of large displacement and it should be solved with perturbation parameter in time domain. This paper compare the dynamic motion responses of a TLP in regular sea waves obtained by applying three method in time domain using MATLAB soft ware. In this paper LindstedtPoincare method (L-P method) is used to solve Nonlinear differential Equation of surge motion considering first-order perturbation. Also modified Euler method (MEM) is used for Solving Nonlinear Equation of motion as numerical method and ordinary differential Equation is used for linear Equation of motion (without Nonlinear term). The results were obtained as responses represent good accordance between results of L-P method and MEM.

Waseem Asghar Khan - One of the best experts on this subject based on the ideXlab platform.

  • new iterative methods for Solving Nonlinear Equation by using homotopy perturbation method
    Applied Mathematics and Computation, 2012
    Co-Authors: Muhammad Aslam Noor, Waseem Asghar Khan
    Abstract:

    In this paper, we suggest and analyze a new class of iterative methods for Solving Nonlinear Equations by using the homotopy perturbation method. Convergence of their method is also considered. Here we also discuss the efficiency index and computational order of convergence of new methods. Several numerical examples are given to illustrate the efficiency and performance of these new methods. These new iterative methods may be viewed as an extension and generalization of the existing methods for Solving Nonlinear Equations.

  • On iterative methods for Nonlinear Equations
    Applied Mathematics and Computation, 2006
    Co-Authors: Muhammad Aslam Noor, Waseem Asghar Khan, Khalida Inayat Noor, Faizan Ahmad
    Abstract:

    Several iterative methods have been suggested and analyzed for Solving Nonlinear Equation f(x)=0. All these methods can be classified as one-step and two-step methods. In this paper, we have suggested and analyzed several two-step methods for Solving Nonlinear Equations. We have also shown that these two-step methods are quadratically convergent. Several numerical examples are given to illustrate this comparison. Our results can be viewed as important refinement and improvement of the previously known results.

Mohammad Reza Tabeshpour - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear dynamic analysis of tlp surge motion using homotopy perturbation method
    Ships and Offshore Structures, 2014
    Co-Authors: Mohammad Reza Tabeshpour, Rahim Shoghi
    Abstract:

    Tension leg platforms (TLPs) are well-known structures for oil exploitation in deep water. One of the current issues in compliant structures in the sea is variation in frequency and structural response due to a Nonlinear parameter in the Equation of motion. Variation of frequency is important in fatigue life study of tethers. A perturbation method is used in contrast to the traditional methods. This method does not require a small parameter for finding surge motion of TLP. In this paper, homotopy perturbation method (HPM) is used to solve a highly Nonlinear differential Equation of surge motion. Calculated responses by HPM are compared with those obtained from both linear and Nonlinear Equations of motion. Numerical method is used for Solving Nonlinear Equation of motion and ordinary differential method is used for linear Equation of motion. It is very useful for a design engineer to have a deep view of Nonlinear vibration behaviour of systems which are naturally Nonlinear like TLP.

  • comparison between linear and Nonlinear models for surge motion of tlp
    The international journal of marine science, 2012
    Co-Authors: Mohammad Reza Tabeshpour, Rahim Shoghi
    Abstract:

    Tension-Leg Platform (TLP) is a vertically moored floating structure. The platform is permanently moored by tendons. Surge Equation of motion of TLP is highly Nonlinear because of large displacement and it should be solved with perturbation parameter in time domain. This paper compare the dynamic motion responses of a TLP in regular sea waves obtained by applying three method in time domain using MATLAB soft ware. In this paper LindstedtPoincare method (L-P method) is used to solve Nonlinear differential Equation of surge motion considering first-order perturbation. Also modified Euler method (MEM) is used for Solving Nonlinear Equation of motion as numerical method and ordinary differential Equation is used for linear Equation of motion (without Nonlinear term). The results were obtained as responses represent good accordance between results of L-P method and MEM.