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Modified Jacobian Newton Iterative Method: Theory and Applications

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  • Jürgen Geiser

Abstract

This article proposes a new approach to the construction of a linearization method based on the iterative operator-splitting method for nonlinear differential equations. The convergence properties of such a method are studied. The main features of the proposed idea are the linearization of nonlinear equations and the application of iterative splitting methods. We present an iterative operator-splitting method with embedded Newton methods to solve nonlinearity. We confirm with numerical applications the effectiveness of the proposed iterative operator-splitting method in comparison with the classical Newton methods. We provide improved results and convergence rates.

Suggested Citation

  • Jürgen Geiser, 2009. "Modified Jacobian Newton Iterative Method: Theory and Applications," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-24, February.
    • Handle: RePEc:hin:jnlmpe:307298
    DOI: 10.1155/2009/307298
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