Solving the quintic by iteration

Solving the quintic by iteration

Equations that can be solved using iterated rational maps are characterized: an equation is ‘computable’ if and only if its Galois group is within A5 of solvable. We give explicitly a new solution to the quintic polynomial, in which the transcendental inversion of the icosahedral map (due to Hermite and Kronecker) is replaced by a purely iterative algorithm. The algorithm requires a rational ma...

Solving the Quintic by Iteration in Three Dimensions

The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S5. Induced by its five-dimensional linear permutation representation is a three-dimensional projective action. A mapping of complex projective 3-space with this S5 symmetry can provide the requisite symmetry-breaking tool. The article describes some of ...

Solving time-fractional chemical engineering equations by modified variational iteration method as fixed point iteration method

The variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The ob...

The variational iteration method for solving Nagumo telegraph equation

Solving the Fisher’s Equation by Means of Variational Iteration Method

In this paper, we consider variational iteration method (VIM) to obtain exact solution to the Fisher’s equation. The variational iteration method is based on Lagrange multipliers for identification of optimal value of parameters in a functional. Using this method, it is possible to find the exact solution or an approximate solution of the problem.