Abstract:
Delay differential equations (denoted as DDE) have a wide range of application in
science and engineering. They arise when the rate of change of a time-dependent process
in its mathematical modeling is not only determined by its present state but also by a
certain past state. Recent studies in such diverse fields as biology, economy, physics and
economics have shown that DDEs play an important role in explaining many different
phenomena. In particular they turn out to be fundamental when ODE-based models fail.
In this research, the solution of a delay differential equation is presented by means of a
homotopy perturbation method. This method is used for solving m
order delay
differential equation by introducing homotopy parameter say p which is taken the values
from 0 to 1.This can be done by constructing a convex homotopy to solve non- linear
equations without need of linearization process. Then the coefficients of like powers of
the parameter p are equated. After this procedure, the m
ii
th
order delay differential
equations were integrated m times to find each approximate solution by using the initial
conditions. In general, three examples are forwarded and evaluated. These results reveal
that the proposed method is very effective and simple to perform and it provides speedy
iterations convergence towards to the exact solution.