Optimal Methods for Finding Simple and Multiple Roots of Nonlinear Equations and their Basins of Attraction
نویسندگان
چکیده
منابع مشابه
Basins of attraction for several methods to find simple roots of nonlinear equations
There are many methods for solving a nonlinear algebraic equation. The methods are classified by the order, informational efficiency and efficiency index. Here we consider other criteria, namely the basin of attraction of the method and its dependence on the order. We discuss several third and fourth order methods to find simple zeros. The relationship between the basins of attraction and the c...
متن کاملBasins of attraction for several third order methods to find multiple roots of nonlinear equations
There are several third order methods for solving a nonlinear algebraic equation having roots of a givenmultiplicitym. Here we compare a recent family of methods of order three to Euler– Cauchy’s method which is found to be the best in the previous work. There are fewer fourth order methods for multiple roots but we will not include them here. Published by Elsevier Inc.
متن کاملCorrigendum to "Basins of attraction for optimal eighth-order methods to find simple roots of nonlinear equations"
Several optimal eighth order methods to obtain simple roots are analyzed. The methods are based on two step, fourth order optimal methods and a third step of modified Newton. The modification is performed by taking an interpolating polynomial to replace either f ðznÞ or f ðznÞ. In six of the eight methods we have used a Hermite interpolating polynomial. The other two schemes use inverse interpo...
متن کاملexistence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types
بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
15 صفحه اولTHIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS
In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.
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ژورنال
عنوان ژورنال: The Nepali Mathematical Sciences Report
سال: 2020
ISSN: 2392-411X
DOI: 10.3126/nmsr.v37i1-2.34065