scholarly journals Variational Iterative Method Applied to Variational Problems with Moving Boundaries

2012 ◽  
Vol 03 (05) ◽  
pp. 395-402 ◽  
Author(s):  
Fateme Ghomanjani ◽  
Sara Ghaderi
Keyword(s):  
Iterative Method ◽  
Variational Problems ◽  
Moving Boundaries ◽  
Variational Iterative Method

scholarly journals A new technology for solving diffusion and heat equations

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 133-140 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Feng Gao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Integral Transform ◽  
New Technology ◽  
Approximate Solutions ◽  
Heat Equations ◽  
Sumudu Transform ◽  
First Time ◽  
Variational Iterative Method

In this paper, a new technology combing the variational iterative method and an integral transform similar to Sumudu transform is proposed for the first time for solutions of diffusion and heat equations. The method is accurate and efficient in development of approximate solutions for the partial differential equations.

scholarly journals SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Atika Radid ◽  
Karim Rhofir
Keyword(s):  
Iterative Method ◽  
Adomian Decomposition Method ◽  
Time Interval ◽  
Time Intervals ◽  
Nonlinear Functional ◽  
Adomian Decomposition ◽  
Wide Range ◽  
Functional Problem ◽  
New Iterative Method ◽  
Variational Iterative Method

Our aim in this paper is to propose an SOR-like new iterative method by introducing a relaxation parameter ω to improve the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [J. Math. Anal. Appl. 316 (2006) 753–763] in order to solve two problems. The first one is the problem of the spread of a nonfatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of prey and predator. The proposed method is not limited to these two problems but can be applicable to a wide range of systems of nonlinear functional problem. The results, for different values of ω, show that we found some known methods and our method compared to methods using the calculation of special polynomials and derivatives like the Adomian decomposition method (ADM), the calculation of the Lagrange multiplier as in the variational iterative method (VIM), or the construction of a homotopy as in the homotopy perturbation method (HPM) has several advantages, such as very effective and very simple to implement. Unfortunately, these methods do not guarantee a valid approximation in large time interval. To overcome this, we applied our method for approximating the solution of the problems in a sequence of time intervals as a multistage approach. Some numerical results are presented with plots according to the parameter ω.

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