On new iterative method for solving systems of nonlinear equations

Abstract  Solving systems of nonlinear equations is a relatively complicated problem for which a number of different approaches have
been proposed. In this paper, we employ the Homotopy Analysis Method (HAM) to derive a family of iterative methods for solving
systems of nonlinear algebraic equations. Our approach yields second and third order iterative methods which are more efficient
than their classical counterparts such as Newton’s, Chebychev’s and Halley’s methods.

• Content Type Journal Article
• Category Original Paper
• DOI 10.1007/s11075-009-9342-8
• Authors
  
  
  • Fadi Awawdeh, Hashemite University Zarqa Jordan
  
  

• Journal Numerical Algorithms
• Online ISSN 1572-9265
• Print ISSN 1017-1398

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Original source : http://www.springerlink.com/content/6804745r423t26...

Non-linear dynamic analyses by meshless local Petrov-Galerkin formulations

In this work, meshless methods based on the local Petrov-Galerkin approach are proposed for the solution of dynamic problems considering elastic and elastoplastic materials. Formulations adopting the Heaviside step function and the Gaussian weight function as the test functions in the local weak form are considered. The moving least-square method is used for the approximation of physical quantities in the local integral equations. After spatial discretization is carried out, a non-linear system of ordinary differential equations of second order is obtained. This system is solved by Newmark/Newton-Raphson techniques. At the end of the paper numerical results are presented, illustrating the potentialities of the proposed methodologies. Copyright © 2009 John Wiley & Sons, Ltd.

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Original source : http://dx.doi.org/10.1002%2Fnme.2756...

Accurate and efficient simulation of transport in multidimensional flow

A new numerical method to obtain high-order approximations of the solution of the linear advection equation in multidimensional problems is presented. The proposed conservative formulation is explicit and based on a single updating step. Piecewise polynomial spatial discretization using Legendre polynomials provides the required spatial accuracy. The updating scheme is built from the functional approximation of the exact solution of the advection equation and a direct evaluation of the resulting integrals. The numerical details for the schemes in one and two spatial dimensions are provided and validated using a set of numerical experiments. Test cases have been oriented to the convergence and the computational efficiency analysis of the schemes. Copyright © 2009 John Wiley & Sons, Ltd.

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Original source : http://dx.doi.org/10.1002%2Ffld.2189...