Convergence Analysis And Applications Of Newton?????S Method And Its Variants For Nonlinear System In Two Dimensions

Abstract

In This Thesis, Newton?��?S Method And Its Variants Used To Solve F(X) = 0 For One Dimension And Two Dimension. We Discussed Convergence And Accelerating Conditions In One Dimension. Then We Drive Newton?��?S Method For Solving Nonlinear System In 2-D. We Also Examined Methods Accelerating Its Convergence In 2-D. That Are Variants Of Newton?��?S Method In 2-D. We Prove Order Of Convergence In 1-D And 2-D. We Applied Series Expansion (Linear And Quadratic) And Construction Techniques For Most Of The Proofs And Derivation. Numerical Experiments Are Provided In Matlab Codes. The Study Shows That Most Of The Methods Accelerating Newton?��?S Convergence Are Cubic Order Both In One Dimension And Two Dimensions. We Also Considered Some Applications In Nonlinear Boundary Value Problems (Bvbs).