scholarly journals NUMERICAL SOLUTION OF LR FUZZY HUNTER-SAXETON EQUATION BY USING HOMOTOPY ANALYSIS METHOD

2012 ◽  
Vol 2 (1) ◽  
pp. 1-10
Author(s):  
Sh. Sadigh Behzadi ◽  
◽  
A. Yildirim ◽  
◽  
Keyword(s):  
Numerical Solution ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Homotopy Analysis

scholarly journals Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Z. Pashazadeh Atabakan ◽  
A. Kazemi Nasab ◽  
A. Kılıçman ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Homotopy Analysis Method ◽  
Existence And Uniqueness ◽  
Lagrange Interpolation ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Uniqueness Of The Solution ◽  
Spectral Homotopy Analysis Method

Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.

Numerical Results of a Flow in a Third Grade Fluid between Two Porous Walls

2009 ◽  
Vol 64 (1-2) ◽  
pp. 59-64 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Tasawar Hayat ◽  
Rahmat Ellahi ◽  
Saleem Asghar
Keyword(s):  
Numerical Solution ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Material Parameter ◽  
Third Grade ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Porous Walls

Series solution for a steady flow of a third grade fluid between two porous walls is given by the homotopy analysis method (HAM). Comparison with the existing numerical solution is shown. It is found that, unlike the numerical solution, the present series solution holds for all values of the material parameter of a third grade fluid.

scholarly journals Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 114
Author(s):  
Emmanuel A. Bakare ◽  
Snehashish Chakraverty ◽  
Radovan Potucek
Keyword(s):  
Numerical Solution ◽  
Homotopy Analysis Method ◽  
Epidemic Model ◽  
Analysis Method ◽  
Sir Epidemic Model ◽  
Deterministic Models ◽  
Interval Model ◽  
Sir Epidemic ◽  
Homotopy Analysis ◽  
Good Agreement

This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). The SIR epidemic model is proposed and solved under different uncertain intervals by the HAM to obtain the numerical solution of the model. Furthermore, the SIR ODE model was transformed into a stochastic differential equation (SDE) model and the results of the stochastic and deterministic models were compared using numerical simulations. The results obtained were compared with the numerical solution and found to be in good agreement. Finally, various simulations were done to discuss the solution.

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