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Title A NEW HOMOTOPY TECHNIQUE FOR SOLVING SYSTEM OF NONLINEAR EQUATIONS

Author(s) Zawar Hussain

Abstract In this study, Örst of all two new optimal fourth order iterative techniques have studied for solving single variable non-linear equations. These techniques need evaluation of one Örst derivative and two function evaluation that satisfy the Kung-Traub conjecture. These numerical techniques are then extended to techniques for solving system of non-linear equations. The establishment and execution of these techniques for solving system of nonlinear equations is based on the concept of element wise vector multiplication and diagonal matrix. In case, Jacobian matrix becomes singular at any stage because of approximation, the above techniques would fail. In order to overcome this di¢ culty, homotopy techniques for solving system of non linear equations were introduced. Theoretical convergence of modiÖed iterative techniques are proved through analysis theorems and numerical convergence through real time applications are provided to test the performance of these techniques.

Type Thesis/Dissertation MS

Faculty Engineering and Computer Science

Department Mathematics

Language English

Publication Date 2024-01-08

Subject Mathematics

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