A New Technique of The q-Homotopy Analysis Method for Solving Non-Linear Initial Value Problems

In this paper, a new procedure of the q-homotopy analysis technique (NTqHAM) was submitted for solving non-linear initial value problems. The NTq-HAM contains just a single convergence control parameter α. To show the dependability and proficiency of the technique, this approach is applied to solve two non-linear IVPs, and the outcomes uncover that the NTq-HAM is more general of the He’s homotopy perturbation technique (HPM) [27] and the He’s HPM is only special case of the NTq-HAM when α = 1

Analytical solution for nonlinear Gas Dynamic equation by Homotopy Analysis Method

In this paper, the Homotopy Analysis Method (HAM) is used to implement the homogeneous gas dynamic equation. The analytical solution of this equation is calculated in form of a series with easily computable components

Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method

The homotopy analysis method is used to find a family of solitary smooth hump solutions of the Camassa-Holm equation. This approximate solution, which is obtained as a series of exponentials, agrees well with the known exact solution. This paper complements the work of Wu & Liao [Wu W, Liao S. Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos, Solitons & Fractals 2005;26:177-85] who used the homotopy analysis method to find a different family of solitary wave solutions

Application of Homotopy Analysis Method for Solving various types of Problems of Ordinary Differential Equations

In this paper, various types of linear, non-linear, homogeneous, non homogeneous problems of ordinary differential equations discussed. Also shown that homotopy analysis method applied successfully for solving non homogeneous and non linear equations

Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri

This study explores the semi-analytical solutions of the third-order dispersive equation with reaction (Fisher-like) term. Recently,the proposed problem has been exactly solved in the literature. Additionally, the semi-analytical solutions are needed to understandthe sensitivity of homotopy based methods in solving the proposed reaction-dispersion equation. Using symbolic computation withcarefully chosen perturbation parameters, the semi-analytical solutions are compared with the exact solutions, in order to show theefficiency of homotopy and Padé techniques. Obtained solutions, which can play key role in modelling reaction in a dispersive medium,are illustrated and discussed.Bu çalışma, üçüncü mertebeden reaksiyon terimli dağılım(dispersive) denkleminin yarı analitik çözümlerini üzerinedir. Son zamanlarda ele alınan problem literatürde tam olarak çözülmüştür. Ayrıca, yarı analitik çözümler, önerilen reaksiyon-dağılım denkleminin çözümünde homotopi temelli yöntemlerin hassasiyetini anlamak için gereklidir. Seçilen pertürbasyon parametreleri ile sembolik hesaplama kullanarak, yarı analitik çözümler, homotopi ve Padé tekniklerinin verimliliğini göstermek için kesin çözümlerle karşılaştırılmaktadır. Elde edilen çözümler dağılımlı ortamda reaksiyon modellemesinde büyük rol oynamaktadır

Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems

In this paper, the homotopy analysis method (HAM) is compared with the homotopy-perturbation method (HPM) and the Adomian decomposition method (ADM) to determine the temperature distribution of a straight rectangular fin with power-law temperature dependent surface heat flux. Comparisons of the results obtained by the HAM with that obtained by the ADM and HPM suggest that both the HPM and ADM are special case of the HAM

Application of Homotopy analysis method to fourth-order parabolic partial differential equations

In this paper, by means of the homotopy analysis method (HAM), the solutions of some fourthorder parabolic partial differential equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple