scholarly journals Numerical Solution of Higher Order Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Muzammal Iftikhar
Keyword(s):  
Boundary Value Problems ◽  
Homotopy Analysis Method ◽  
Present Method ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Higher Order ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

The aim of this paper is to use the homotopy analysis method (HAM), an approximating technique for solving linear and nonlinear higher order boundary value problems. Using HAM, approximate solutions of seventh-, eighth-, and tenth-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results obtained from this method are compared with the exact solutions and other methods (Akram and Rehman (2013), Farajeyan and Maleki (2012), Geng and Li (2009), Golbabai and Javidi (2007), He (2007), Inc and Evans (2004), Lamnii et al. (2008), Siddiqi and Akram (2007), Siddiqi et al. (2012), Siddiqi et al. (2009), Siddiqi and Iftikhar (2013), Siddiqi and Twizell (1996), Siddiqi and Twizell (1998), Torvattanabun and Koonprasert (2010), and Kasi Viswanadham and Raju (2012)) revealing that the present method is more accurate.

scholarly journals The Approximate Solutions of Fredholm Integrodifferential-Difference Equations with Variable Coefficients via Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Seydi Battal Gazi Karakoç ◽  
Aytekin Eryılmaz ◽  
Musa Başbük
Keyword(s):  
Difference Equations ◽  
Homotopy Analysis Method ◽  
Algebraic System ◽  
Numerical Solutions ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

Numerical solutions of linear and nonlinear integrodifferential-difference equations are presented using homotopy analysis method. The aim of the paper is to present an efficient numerical procedure for solving linear and nonlinear integrodifferential-difference equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system.

scholarly journals Solving Famous Nonlinear Coupled Equations with Parameters Derivative by Homotopy Analysis Method

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Sohrab Effati ◽  
Hassan Saberi Nik ◽  
Reza Buzhabadi
Keyword(s):  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Reaction Diffusion Equations ◽  
Analysis Method ◽  
Coupled Equations ◽  
Homotopy Analysis ◽  
Special Case

The homotopy analysis method (HAM) is employed to obtain symbolic approximate solutions for nonlinear coupled equations with parameters derivative. These nonlinear coupled equations with parameters derivative contain many important mathematical physics equations and reaction diffusion equations. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The efficiency and accuracy of the method are verified by using two famous examples: coupled Burgers and mKdV equations. The obtained results show that the homotopy perturbation method is a special case of homotopy analysis method.

Sign in / Sign up

Export Citation Format

Share Document