Halley Irrational-Homotopy Analysis Method

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations

Solving a System of Linear Equations by Homotopy Analysis Method

‎In this paper‎, ‎an efficient algorithm for solving a system of linear‎ ‎equations based on the homotopy analysis method is presented‎. ‎The‎ ‎proposed method is compared with the classical Jacobi iterative‎ ‎method‎, ‎and the convergence analysis is discussed‎. ‎Finally‎, ‎two‎ ‎numerical examples are presented to show the effectiveness of the‎ ‎proposed method.‎

Predictor-corrector Halley method for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative methods for solving nonlinear equations of the type f(x) = 0 by using the technique of updating the solution. This method can be viewed as a predictor– corrector iterative Halley’s method. We also consider the convergence analysis of the proposed method. To illustrate the efficiency of this new method, we gi...

Homotopy Analysis Method for Solving Kdv Equations

A scheme is developed for the numerical study of the Korteweg-de Vries (KdV) and the Korteweg-de Vries Burgers (KdVB) equations with initial conditions by a homotopy approach. Numerical solutions obtained by homotopy analysis method are compared with exact solution. The comparison shows that the obtained solutions are in excellent agreement.

On Convergence of q-Homotopy Analysis Method

The convergence of qhomotopy analysis method (q-HAM) is studied in the present paper. It is proven that under certain conditions the solution of the equation: 1 ∅ , ∅ , 0 associated with the original problem exists as a power series in .So,under a special constraint the q-homotopy analysis method does converge to the exact solution of nonlinear problems. An error estimate is also provided. The ...