Abstract:
This paper mainly present, sixth order Taylor’s method and fifth order
Runge-Kutta method (RK5) for solving initial value problems of first order ordinary
differential equations. The two proposed methods are quite efficient and practically
well suited for solving these problems. In order to verify the accuracy, we compare
numerical solutions with the exact solutions. The numerical solutions are in good
agreement with the exact solutions. Numerical comparisons between Taylor’s method
and Runge-Kutta methods have been presented. The stability and convergence of the
methods have been investigated. Two model examples (linear and non-linear) are
given to demonstrate the reliability and efficiency of the methods. Point wise absolute
errors are obtained by using MATLAB software. The proposed methods also
compared with the existing literatures (RK4) and shows betterment results.
