Computational and numerical simulations for the deoxyribonucleic acid (DNA) model
Raghda A. M. Attia, Dumitru Bǎleanu, Dianchen Lu, Mostafa M. A. Khater, El-Sayed Ahmed
Abstract
<p style='text-indent:20px;'>In this research paper, the modified Khater method, the Adomian decomposition method, and B-spline techniques (cubic, quintic, and septic) are applied to the deoxyribonucleic acid (DNA) model to get the analytical, semi-analytical, and numerical solutions. These solutions comprise much information about the dynamical behavior of the homogenous long elastic rods with a circular section. These rods constitute a pair of the polynucleotide rods of the DNA molecule which are plugged by an elastic diaphragm that demonstrates the hydrogen bond's role in this communication. The stability property is checked for some solutions to show more effective and powerful of obtained solutions. Based on the role of analytical and semi-analytical techniques in the motivation of the numerical techniques to be more accurate, the B-spline numerical techniques are applied by using the obtained exact solutions on the DNA model to show which one of them is more accurate than other, to explain more of the dynamic behavior of the homogenous long elastic rods, and to show the coincidence between the different types of obtained solutions. The obtained solutions verified with Maple 16 & Mathematica 12 by placing them back into the original equations. The performance of these methods shows the power and effectiveness of them for applying to many different forms of the nonlinear evolution equations with an integer and fractional order.