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Numerical solution of nonlinear systems by a general class of iterative methods with application to nonlinear PDEs

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Abstract

A general class of multi-step iterative methods for finding approximate real or complex solutions of nonlinear systems is presented. The well-known technique of undetermined coefficients is used to construct the first method of the class while the higher order schemes will be attained by a frozen Jacobian. The point of attraction theory will be taken into account to prove the convergence behavior of the main proposed iterative method. Then, it will be observed that an m-step method converges with 2m-order. A discussion of the computational efficiency index alongside numerical comparisons with the existing methods will be given. Finally, we illustrate the application of the new schemes in solving nonlinear partial differential equations.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Malik Zaka Ullah & A. S. Al-Fhaid

  2. Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran

    Fazlollah Soleymani

Authors
  1. Malik Zaka Ullah
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  2. Fazlollah Soleymani
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  3. A. S. Al-Fhaid
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Correspondence to Fazlollah Soleymani.

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Ullah, M.Z., Soleymani, F. & Al-Fhaid, A.S. Numerical solution of nonlinear systems by a general class of iterative methods with application to nonlinear PDEs. Numer Algor 67, 223–242 (2014). https://doi.org/10.1007/s11075-013-9784-x

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  • DOI: https://doi.org/10.1007/s11075-013-9784-x

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