A variant of Newton's method with accelerated third-order convergence
نویسندگان
چکیده
منابع مشابه
A modification of Newton method with third-order convergence
In this paper, we present a new modification of Newton method for solving non-linear equations. Analysis of convergence shows that the new method is cubically convergent. Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. Thus, the new method is preferable if the computational costs of the first derivative are equal or more than tho...
متن کاملSome variants of Cauchy’s method with accelerated fourth-order convergence
In this paper, we present some variants of Cauchy’s method for solving non-linear equations. Analysis of convergence shows that the methods have fourth-order convergence. Per iteration the new methods cost almost the same as Cauchy’s method. Numerical results show that the methods can compete with Cauchy’s method. © 2007 Published by Elsevier B.V. MSC: 41A25; 65D99
متن کاملA Class of Two-Step Newton’s Methods with Accelerated Third Order Convergence
In this work we propose an improvement to the popular Newton’s method based on the contra-harmonic mean while using quadrature rule derived from a Ostrowski-Gräuss type inequality developed in [19]. The order of convergence of this method for solving non-linear equations which have simple roots is shown to be three. Computer Algebra Systems (CAS), such as MAPLE 18 package, can be used successfu...
متن کاملA Family of Iterative Methods with Accelerated Eighth-Order Convergence
We propose a family of eighth-order iterative methods without memory for solving nonlinear equations. The new iterative methods are developed by using weight function method and using an approximation for the last derivative, which reduces the required number of functional evaluations per step. Their efficiency indices are all found to be 1.682. Several examples allow us to compare our algorith...
متن کاملNonstandard explicit third-order Runge-Kutta method with positivity property
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2000
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(00)00100-2