APPLICATION OF MULTI-STEP DIFFERENTIAL TRANSFORM METHOD FOR THE ANALYTICAL AND NUMERICAL SOLUTIONS OF THE DENSITY DEPENDENT NAGUMO TELEGRAPH EQUATION

作者：Erturk Vedat Suat^*; Odibat Zaid M; Momani Shaher

来源：Romanian Journal of Physics, 2012, 57(7-8): 1065-1078.

• Nagumo telegraph equation
• Differential Transform Method
• Numerical solution

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.

• 出版日期2012