Author(s):
Ravindra Singh, Omwati Rana , Yogesh Kumar Sharma , Shiv Shankar Gaur
Abstract:
Numerical approximation methods have been developed to linear differential
equation with initial condition. The comparison of the results has been done among Euler’s
method, modified Euler’s method and RK-4 with the help of Scilab software 6.1.1. RK-4
method is effective enough to reach more accuracy in the result. The Runge-Kutta
method attempts to overcome the problem of the Euler's method, and modified Euler's method
and the study shows that in all cases RK-4 method improves to a great extent, than those by
the Euler method and Modified Euler’s Method. For RK-4 the approximation accuracy is
proportional to the fourth power of the step size, thus making it a powerful and widely used
numerical method also this method gives us higher accuracy without performing more
calculations. Three different values of the step size have been taken. It is observed that smaller
values of step size give better result; in all cases RK-4 method fits best as compared to others.
The nature of the plot obtained by directly matches with the approximation solutions. It is
observed that RK-4 method is suitable for obtaining the accurate solution of ODEs when the
taken step sizes are too much small; since smaller h reduces the error.
Pages: 471-479
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