scholarly journals Approximate Analytical Solutions of Nonlinear Korteweg-de Vries Equations Using Multistep Modified Reduced Differential Transform Method

2020 ◽  
Vol 8 (2A) ◽  
pp. 9-16
Author(s):  
Che Haziqah Che Hussin ◽  
Ahmad Izani Md Ismail ◽  
Adem Kilicman ◽  
Amirah Azmi
Keyword(s):  
Analytical Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Approximate Analytical Solutions ◽  
Differential Transform ◽  
De Vries ◽  
Reduced Differential Transform Method

scholarly journals Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhoujin Cui ◽  
Zisen Mao ◽  
Sujuan Yang ◽  
Pinneng Yu
Keyword(s):  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Time Derivative ◽  
Differential Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Differential Transform ◽  
Reduced Differential Transform Method

The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.

Prediction of Phagocyte Transmigration for Foreign Body Responses to Subcutaneous Biomaterial Implantations Using Differential Transform Method

2017 ◽  
Vol 32 ◽  
pp. 98-114
Author(s):  
Olurotimi Adeleye ◽  
Olatutu Olawale ◽  
Gbeminiyi Sobamowo
Keyword(s):  
Foreign Body ◽  
Analytical Solutions ◽  
Predictive Models ◽  
Direct Relationship ◽  
Differential Transform Method ◽  
Model Parameters ◽  
Transform Method ◽  
Biochemical Processes ◽  
Approximate Analytical Solutions ◽  
Differential Transform

The complexity of the multiple interactive reactions of various cells/proteins and biochemical processes during phagocyte transmigration for foreign body responses to subcutaneous biomaterial implants have been studied through developed kinetics-based predictive models which have been numerically analyzed. However, the need for direct relationship between the kinetic-based predictive models parameters and the requirements for continuous insights into the significance of various process parameters affecting the phenomena have led to the quest for developing analytical solutions. Therefore, in this work, differential transform method is used to develop analytical solutions for the prediction of phagocyte transmigration for foreign body responses to subcutaneous biomaterial implants. The approximate analytical solutions are used to study the effect of various model parameters on phagocyte transmigration to foreign body responses in biomaterial implantation. The results of the analytical solutions are agreement with the results of the previous studies.

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