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A novel method for solving nonlinear equations
American Mathematical Society , 2011 Joint Mathematics Meetings, New Orleans ,USA (2010)
  • Mohsen Mahmood Doroodchi, Cardinal Stritch University
  • Habibolla Latifizadeh, Shiraz University of Technology
Abstract

The confluence of modern mathematics and symbolic computation has posed a challenge to develop methodologies capable of handling strongly nonlinear equations which cannot be successfully dealt with by classical methods. The current proposed method is uniquely quali ed to address this challenge. The idea of Variational Iteration Method (VIM) is to construct a correction functional by a general Lagrange multiplier which can be identi ed optimally via the variational theory. The novel technique proposed in this paper provides a sequence of functions which converges to the exact solution of the nonlinear problem without requiring small parameters as the perturbation techniques and the general Lagrange multiplier in Variational Iteration Method. As an advantage of the method over decomposition procedure of Adomian, it provides the solution of the problem without calculating Adomian's polynomials. This technique solves the problem without any need to discretization of the variables. Therefore, it is not a ected by computation round-o errors. It is capable of greatly reducing the volume of the computational work compared to classical methods while still maintaining high accuracy of the numerical solution.

Publication Date
Fall October 21, 2010
Citation Information
Mohsen Mahmood Doroodchi and Habibolla Latifizadeh. "A novel method for solving nonlinear equations" American Mathematical Society , 2011 Joint Mathematics Meetings, New Orleans ,USA (2010)
Available at: http://works.bepress.com/habib_latifizadeh/16/