The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform

Quan Nguyen - One of the best experts on this subject based on the ideXlab platform.

  • Minimum volume of the longitudinal fin with rectangular and triangular profile by a Modified Newton-Raphson method
    2016
    Co-Authors: Quan Nguyen, Son Hoai Nguyen, Tuan Quoc Nguyen
    Abstract:

    The minimum volume of nonlinear longitudinal fin with rectangular and triangular profile by using the Modified Newton-Raphson method is present in this paper. The dimension of the fin profile is regarded as optimization variables. Furthermore, a mechanism called “volume updating” is added into the Modified Newton-Raphson algorithm to obtain the minimum volume of the fin. Two examples are illustrated to demonstrate the proposed method. The obtained results showed that the proposed method use efficiently and accurately in finding the minimum volume of the nonlinear longitudinal fin problem with the rectangular and triangle profile.

  • design of a longitudinal cooling fin with minimum volume by a Modified Newton raphson method
    Applied Thermal Engineering, 2016
    Co-Authors: Quan Nguyen, Ching-yu Yang
    Abstract:

    Abstract In this paper, the minimal volume of nonlinear longitudinal cooling fin design problem by using a Modified Newton–Raphson method is presented. The profile of the fin is built by B-spline curve in which the control points of the B-spline curve are regarded as optimization variables. Additionally, a mechanism called “volume updating” is added into the Modified Newton–Raphson algorithm to obtain the minimum volume of the fin. Four cases with the different boundary conditions and thermal properties of the longitudinal fin are presented to demonstrate the proposed method. The results show that the optimal fin obtained by the proposed method is in good agreement with Schmidt's (1926) result and is better than that of Azarkish, et al. (2010). It is concluded that the B-spline with the second degree and three control points could be used enough to find the minimum volume of the longitudinal fin for the linear and nonlinear fin design problems. From the results obtained in four cases, it appears that the proposed method is an efficient and accurate method in finding the minimum volume of the nonlinear longitudinal cooling fin design problem.

  • Design of a longitudinal cooling fin with minimum volume by a Modified Newton–Raphson method
    Applied Thermal Engineering, 2016
    Co-Authors: Quan Nguyen, Ching-yu Yang
    Abstract:

    Abstract In this paper, the minimal volume of nonlinear longitudinal cooling fin design problem by using a Modified Newton–Raphson method is presented. The profile of the fin is built by B-spline curve in which the control points of the B-spline curve are regarded as optimization variables. Additionally, a mechanism called “volume updating” is added into the Modified Newton–Raphson algorithm to obtain the minimum volume of the fin. Four cases with the different boundary conditions and thermal properties of the longitudinal fin are presented to demonstrate the proposed method. The results show that the optimal fin obtained by the proposed method is in good agreement with Schmidt's (1926) result and is better than that of Azarkish, et al. (2010). It is concluded that the B-spline with the second degree and three control points could be used enough to find the minimum volume of the longitudinal fin for the linear and nonlinear fin design problems. From the results obtained in four cases, it appears that the proposed method is an efficient and accurate method in finding the minimum volume of the nonlinear longitudinal cooling fin design problem.

Tamer Bagatur - One of the best experts on this subject based on the ideXlab platform.

  • Modified Newton raphson solution for dispersion equation of transition water waves
    Journal of Coastal Research, 2007
    Co-Authors: Tamer Bagatur
    Abstract:

    Abstract Modified Newton–Raphson solution for dispersion equation of transition water waves is proposed for practical applications. The wave dispersion equation is a nonlinear equation. Therefore, one has to apply a time-consuming trial-and-error method. However, it may be solved by utilizing an iterative technique commonly referred to as Newton–Raphson (NR) iteration technique and Chebyshev approximation, which are used to solve the system of nonlinear equations. Chebyshev approximation has the advantage of requiring less iteration. In this study, a numerical solution model based on utilizing Modified NR technique with Chebyshev approximation to determine value of the wave number (k) is developed. It is shown how iteration problems can be solved by Modified NR technique with Chebyshev approximation. This computational model is applied by computer programs that have visual basic (VBA) code prepared under the Microsoft Excel Macro. The wave dispersion equation for transition water waves were solved by modi...

  • Modified Newton–Raphson Solution for Dispersion Equation of Transition Water Waves
    Journal of Coastal Research, 2007
    Co-Authors: Tamer Bagatur
    Abstract:

    Abstract Modified Newton–Raphson solution for dispersion equation of transition water waves is proposed for practical applications. The wave dispersion equation is a nonlinear equation. Therefore, one has to apply a time-consuming trial-and-error method. However, it may be solved by utilizing an iterative technique commonly referred to as Newton–Raphson (NR) iteration technique and Chebyshev approximation, which are used to solve the system of nonlinear equations. Chebyshev approximation has the advantage of requiring less iteration. In this study, a numerical solution model based on utilizing Modified NR technique with Chebyshev approximation to determine value of the wave number (k) is developed. It is shown how iteration problems can be solved by Modified NR technique with Chebyshev approximation. This computational model is applied by computer programs that have visual basic (VBA) code prepared under the Microsoft Excel Macro. The wave dispersion equation for transition water waves were solved by modi...

Minhong Chen - One of the best experts on this subject based on the ideXlab platform.

  • Modified Newton mdpmhss method for solving nonlinear systems with block two by two complex symmetric jacobian matrices
    Numerical Algorithms, 2019
    Co-Authors: Minhong Chen
    Abstract:

    In this study, an efficient iterative method is given to solve large sparse nonlinear systems with block two-by-two complex symmetric Jacobian matrices. Based on the double-parameter preconditioned MHSS (DPMHSS) method, a Modified double-parameter preconditioned MHSS (MDPMHSS) method is developed to solve a class of linear systems with block two-by-two complex coefficient matrices. Then, a Modified Newton-MDPMHSS method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices is obtained, which MDPMHSS is employed as the inner iteration and the Modified Newton method is employed as the outer iteration. Local convergence analysis is given for the new present method under Holder condition, which is weaker than Lipschitz condition. At last, numerical results are reported to verify the efficiency of the new method.

  • on Modified Newton dgpmhss method for solving nonlinear systems with complex symmetric jacobian matrices
    Computers & Mathematics With Applications, 2018
    Co-Authors: Minhong Chen
    Abstract:

    Abstract This paper aims to give an efficient iterative method for solving large sparse nonlinear system with complex symmetric Jacobian matrix. Employing the double-parameter generalized preconditioned MHSS (DGPMHSS) method as the inner iteration, and using the Modified Newton method as the outer iteration , we establish a Modified Newton–DGPMHSS method for solving nonlinear system with complex symmetric Jacobian matrix. For the new presented method, we provide the local convergence analysis under Holder condition, which is weaker than Lipschitz condition. Furthermore, we compare our new method with the Modified Newton–PMHSS method, which is a considerable method for dealing with large sparse nonlinear system with complex symmetric Jacobian matrix, and the numerical results show the efficiency of our new method.

  • On Modified Newton–DGPMHSS method for solving nonlinear systems with complex symmetric Jacobian matrices
    Computers & Mathematics with Applications, 2018
    Co-Authors: Minhong Chen
    Abstract:

    Abstract This paper aims to give an efficient iterative method for solving large sparse nonlinear system with complex symmetric Jacobian matrix. Employing the double-parameter generalized preconditioned MHSS (DGPMHSS) method as the inner iteration, and using the Modified Newton method as the outer iteration , we establish a Modified Newton–DGPMHSS method for solving nonlinear system with complex symmetric Jacobian matrix. For the new presented method, we provide the local convergence analysis under Holder condition, which is weaker than Lipschitz condition. Furthermore, we compare our new method with the Modified Newton–PMHSS method, which is a considerable method for dealing with large sparse nonlinear system with complex symmetric Jacobian matrix, and the numerical results show the efficiency of our new method.

  • Modified Newton-NSS method for solving systems of nonlinear equations
    Numerical Algorithms, 2017
    Co-Authors: Ping-fei Dai, Minhong Chen
    Abstract:

    By making use of the normal and skew-Hermitian splitting (NSS) method as the inner solver for the Modified Newton method, we establish a class of Modified Newton-NSS method for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. Under proper conditions, the local convergence theorem is proved. Furthermore, the successive-overrelaxation (SOR) technique has been proved quite successfully in accelerating the convergence rate of the NSS or the Hermitian and skew-Hermitian splitting (HSS) iteration method, so we employ the SOR method in the NSS iteration, and we get a new method, which is called Modified Newton SNSS method. Numerical results are given to examine its feasibility and effectiveness.

  • Semilocal convergence analysis for the Modified Newton-HSS method under the Holder condition
    Numerical Algorithms, 2015
    Co-Authors: Minhong Chen, Rong-fei Lin
    Abstract:

    The present paper is concerned with theoretical properties of the Modified Newton-HSS method for large sparse non-Hermitian positive definite systems of nonlinear equations. Assuming that the nonlinear operator satisfies the H?lder continuity condition, a new semilocal convergence theorem for the Modified Newton-HSS method is established. The H?lder continuity condition is milder than the usual Lipschitz condition. The semilocal convergence theorem is established by using the majorizing principle, which is based on the concept of majorizing sequence given by Kantorovich. Two real valued functions and two real sequences are used to establish the convergence criterion. Furthermore, a numerical example is given to show application of our theorem.

Ching-yu Yang - One of the best experts on this subject based on the ideXlab platform.

  • design of a longitudinal cooling fin with minimum volume by a Modified Newton raphson method
    Applied Thermal Engineering, 2016
    Co-Authors: Quan Nguyen, Ching-yu Yang
    Abstract:

    Abstract In this paper, the minimal volume of nonlinear longitudinal cooling fin design problem by using a Modified Newton–Raphson method is presented. The profile of the fin is built by B-spline curve in which the control points of the B-spline curve are regarded as optimization variables. Additionally, a mechanism called “volume updating” is added into the Modified Newton–Raphson algorithm to obtain the minimum volume of the fin. Four cases with the different boundary conditions and thermal properties of the longitudinal fin are presented to demonstrate the proposed method. The results show that the optimal fin obtained by the proposed method is in good agreement with Schmidt's (1926) result and is better than that of Azarkish, et al. (2010). It is concluded that the B-spline with the second degree and three control points could be used enough to find the minimum volume of the longitudinal fin for the linear and nonlinear fin design problems. From the results obtained in four cases, it appears that the proposed method is an efficient and accurate method in finding the minimum volume of the nonlinear longitudinal cooling fin design problem.

  • Design of a longitudinal cooling fin with minimum volume by a Modified Newton–Raphson method
    Applied Thermal Engineering, 2016
    Co-Authors: Quan Nguyen, Ching-yu Yang
    Abstract:

    Abstract In this paper, the minimal volume of nonlinear longitudinal cooling fin design problem by using a Modified Newton–Raphson method is presented. The profile of the fin is built by B-spline curve in which the control points of the B-spline curve are regarded as optimization variables. Additionally, a mechanism called “volume updating” is added into the Modified Newton–Raphson algorithm to obtain the minimum volume of the fin. Four cases with the different boundary conditions and thermal properties of the longitudinal fin are presented to demonstrate the proposed method. The results show that the optimal fin obtained by the proposed method is in good agreement with Schmidt's (1926) result and is better than that of Azarkish, et al. (2010). It is concluded that the B-spline with the second degree and three control points could be used enough to find the minimum volume of the longitudinal fin for the linear and nonlinear fin design problems. From the results obtained in four cases, it appears that the proposed method is an efficient and accurate method in finding the minimum volume of the nonlinear longitudinal cooling fin design problem.

Nitin Kalra - One of the best experts on this subject based on the ideXlab platform.

  • A Modified Newton–Özban Composition for Solving Nonlinear Systems
    International Journal of Computational Methods, 2019
    Co-Authors: Rajni Sharma, Janak Raj Sharma, Nitin Kalra
    Abstract:

    In this work, a Modified Newton–Ozban composition of convergence order six for solving nonlinear systems is presented. The first two steps of proposed scheme are based on third-order method given ...

  • A Modified Newton–Özban Composition for Solving Nonlinear Systems
    International Journal of Computational Methods, 2019
    Co-Authors: Rajni Sharma, Janak Raj Sharma, Nitin Kalra
    Abstract:

    In this work, a Modified Newton–Özban composition of convergence order six for solving nonlinear systems is presented. The first two steps of proposed scheme are based on third-order method given by Özban [Özban, A. Y. [2004] “Some new variants of Newton’s method,” Appl. Math. Lett. 17, 677–682.] for solving scalar equations. Computational efficiency of the presented method is discussed and compared with well-known existing methods. Numerical examples are studied to demonstrate the accuracy of the proposed method. The basins of attraction of some of the existing methods along with the proposed method are given to exhibit their performance.