scholarly journals Approximate analytical solutions of singularly perturbed fourth order boundary value problems using differential transform method

2013 ◽  
Vol 25 (3) ◽  
pp. 257-265 ◽  
Author(s):  
Essam R. El-Zahar
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Differential Transform Method ◽  
Singularly Perturbed ◽  
Transform Method ◽  
Approximate Analytical Solutions ◽  
Differential Transform

scholarly journals Numerical Treatment of Singularly Perturbed Two-Point Boundary Value Problems by Using Differential Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Nurettin Doğan ◽  
Vedat Suat Ertürk ◽  
Ömer Akın
Keyword(s):  
Boundary Value Problems ◽  
Present Method ◽  
Boundary Value ◽  
Transformation Method ◽  
High Accuracy ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Transform Method ◽  
Differential Transform ◽  
First Time

Differential transform method is adopted, for the first time, for solving linear singularly perturbed two-point boundary value problems. Four numerical examples are given to demonstrate the effectiveness of the present method. Results show that the numerical scheme is very effective and convenient for solving a large number of linear singularly perturbed two-point boundary value problems with high accuracy.

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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