scholarly journals The discrete homotopy perturbation Sumudu transform method for solving partial difference equations

2019 ◽  
Vol 12 (3) ◽  
pp. 615-624 ◽  
Author(s):  
Figen Özpinar ◽  
◽  
Fethi Bin Muhammad Belgacem ◽  
Keyword(s):  
Difference Equations ◽  
Transform Method ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Homotopy Perturbation ◽  
Sumudu Transform

scholarly journals Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

2020 ◽  
Vol 9 (1) ◽  
pp. 370-381
Author(s):  
Dinkar Sharma ◽  
Gurpinder Singh Samra ◽  
Prince Singh
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Present Scheme ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

Chaotic Dynamics of Partial Difference Equations with Polynomial Maps

2021 ◽  
Vol 31 (09) ◽  
pp. 2150133
Author(s):  
Haihong Guo ◽  
Wei Liang
Keyword(s):  
Dynamical Systems ◽  
Computer Simulations ◽  
Difference Equations ◽  
Chaotic Dynamics ◽  
Discrete Dynamical Systems ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Polynomial Maps ◽  
Expansion Theory ◽  
Theoretical Results

In this paper, chaotic dynamics of a class of partial difference equations are investigated. With the help of the coupled-expansion theory of general discrete dynamical systems, two chaotification schemes for partial difference equations with polynomial maps are established. These controlled equations are proved to be chaotic either in the sense of Li–Yorke or in the sense of both Li–Yorke and Devaney. One example is provided to illustrate the theoretical results with computer simulations for demonstration.

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