APPLICATION OF MULTI-STEP DIFFERENTIAL TRANSFORM METHOD FOR THE ANALYTICAL AND NUMERICAL SOLUTIONS OF THE DENSITY DEPENDENT NAGUMO TELEGRAPH EQUATION
ROMANIAN JOURNAL OF PHYSICS, cilt.57, sa.7-8, ss.1065-1078, 2012 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 57 Sayı: 7-8
- Basım Tarihi: 2012
- Dergi Adı: ROMANIAN JOURNAL OF PHYSICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1065-1078
- Anahtar Kelimeler: Nagumo telegraph equation, Differential Transform Method, Numerical solution, REACTION-DIFFUSION EQUATION, TRANSMISSION LINE, PROPAGATION, SYSTEMS
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
The Differential Transform Method (DTM) is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form. The multi-step DTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions. In this paper, this new algorithm is applied to a class of density dependent diffusion equations with memory-delay effect. The multi-step differential transform solutions for various strengths of the density dependence along with bounds on the range of the convergence are obtained. The numerical solutions are obtained by the Runge-Kutta-Fehlberg 45 method. Then, a comparative study between the multi-step DTM and Runge-Kutta-Fehlberg 45 method is presented. The results demonstrate reliability and efficiency of the algorithm developed. Finally, the dependence of the traveling wave solutions on various parameters, particularly the memory-delay term, is discussed.