A New Three Step Iterative Method without Second Derivative for Solving Nonlinear Equations

In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples

Homotopy Perturbation Method with an Auxiliary Term

The two most important steps in application of the homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. The homotopy equation should be such constructed that when the homotopy parameter is zero, it can approximately describe the solution property, and the initial solution can be chosen with an unknown parameter, which is determined after one or two iterations. This paper suggests an alternative approach to construction of the homotopy equation with an auxiliary term; Dufing equation is used as an example to illustrate the solution procedure

New two-step predictor-corrector method with ninth order convergence for solving nonlinear equations

In this paper, we suggest and analyze a new two-step predictor-corrector type iterative method for solving nonlinear equations of the type. This method based on a Halley and Householder iterative method and using predictor corrector technique. The convergence analysis of our method is discussed. It is established that the new method has convergence order nine. Numerical tests show that the new methods are comparable with the well known existing methods and gives better results

A New Three Step Iterative Method without Second Derivative for Solving Nonlinear Equations

In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples

Two New Predictor-Corrector Iterative Methods with Third- and Ninth-Order Convergence for Solving Nonlinear Equations

In this paper, we suggest and analyze two new predictor-corrector iterative methods with third and ninth-order convergence for solving nonlinear equations. The first method is a development of [M. A. Noor, K. I. Noor and K. Aftab, Some New Iterative Methods for Solving Nonlinear Equations, World Applied Science Journal, 20(6),(2012):870-874.] based on the trapezoidal integration rule and the centroid mean. The second method is an improvement of the first new proposed method by using the technique of updating the solution. The order of convergence and corresponding error equations of new proposed methods are proved. Several numerical examples are given to illustrate the efficiency and performance of these new methods and compared them with the Newton's method and other relevant iterative methods. Keywords: Nonlinear equations, Predictor–corrector methods, Trapezoidal integral rule, Centroid mean, Technique of updating the solution; Order of convergence

Metode Iterasi Dua Titik Berparameter Real dengan orde Konvergensi Optimal

Pada artikel ini, sebuah metode iterasi baru dikonstruksi menggunakan generalisasi metode iterasi dua titik dengan delapan parameter real A, B, C, D, E, F, G, dan H. Generalisasi bentuk metode iterasi dilakukan untuk menentukan orde konvergensi optimal dengan mengganti nilai-nilai parameter real. Hasil kajian menunjukkan bahwa metode iterasi mempunyai orde konvergensi tiga yang melibatkan delapan parameter real. Selanjutnya orde konvergensi metode iterasi meningkat dengan mengganti  A = E dan B = F + 2  sehingga hanya melibatkan enam parameter real. Selain itu, metode iterasi memerlukan  tiga evaluasi fungsi dan memiliki indeks efisiensi sebesar 41/3 » 1,5874. Simulasi numerik diberikan untuk menguji performasi metode baru dengan menggunakan beberapa fungsi real. Performa metode iterasi baru tersebut adalah jumlah iterasi, orde konvergensi yang dihitung secara komputasi dan nilai mutlak fungsi. Selanjutnya, ukuran-ukuran performasi metode iterasi baru dibandingkan dengan Metode Newton, Metode Chun, Metode Newton Ganda dan Metode Noor. Hasil simulasi numerik menunjukkan bahwa metode iterasi baru mempunyai performa lebih baik dibandingkan dengan metode iterasi lainny

Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method

A homotopy perturbation transformation method (HPTM) which is based on homotopy perturbation method and Laplace transform is first applied to solve the approximate solution of the fractional nonlinear equations. The nonlinear terms can be easily handled by the use of He's polynomials. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm

New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus

This reprint focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems. It is impossible to deny that fractional behaviour exists in nature. Any phenomenon that has a pulse, rhythm, or pattern appears to be a fractal. The 17 papers that were published and are part of this volume provide credence to that claim. A variety of topics illustrate the use of fractional calculus in a range of disciplines and offer sufficient coverage to pique every reader's attention