scholarly journals Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method

2016 ◽  
Vol 40 (13-14) ◽  
pp. 6639-6649 ◽  
Author(s):  
Mehmet Giyas Sakar ◽  
Fatih Uludag ◽  
Fevzi Erdogan
Keyword(s):  
Perturbation Method ◽  
Numerical Solution ◽  
Homotopy Perturbation Method ◽  
Nonlinear Pdes ◽  
Proportional Delays ◽  
Homotopy Perturbation

scholarly journals AN ACCURATE SOLUTION TO THE LOTKA-VOLTERRA EQUATIONS BY MODIFIED HOMOTOPY PERTURBATION METHOD

2012 ◽  
Vol 09 ◽  
pp. 326-333 ◽  
Author(s):  
M. S. H. CHOWDHURY ◽  
M. M. RAHMAN
Keyword(s):  
Perturbation Method ◽  
Numerical Solution ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Accurate Solution ◽  
Volterra Equations ◽  
Algebraic Equations ◽  
Time Intervals ◽  
Homotopy Perturbation

In this paper, we suggest a method to solve the multispecies Lotka-Voltera equations. The suggested method, which we call modified homotopy perturbation method, can be considered as an extension of the homotopy perturbation method (HPM) which is very efficient in solving a varety of differential and algebraic equations. The HPM is modified in order to obtain the approximate solutions of Lotka-Voltera equation response in a sequence of time intervals. In particular, the example of two species is considered. The accuracy of this method is examined by comparison with the numerical solution of the Runge-Kutta-Verner method. The results prove that the modified HPM is a powerful tool for the solution of nonlinear equations.

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