• Dr.S.KARUNANITHI
• N.GAJALAKSHMI
• M.MALARVIZHI
• T.DHIVYA

This Paper mainly presents single-step method Taylor’s series method, Picard’s method and Multistep methods Milnes method and Adams Moulton Predictor-Corrector method, for solving initial value problems (IVP) for ordinary differential equations (ODE). The four proposed methods are quite efficient and practically well suited for solving these problems. To verify the accuracy, we compare numerical solutions with the exact solutions. The numerical solutions are in good agreement with the exact solutions. Numerical comparison between Taylor’s series method, Adams Moulton Predictor-Corrector method, Milnes method and Picard’s method have been presented. Also, we compare the performance and the computational effort of such methods to achieve higher accuracy in the solution, the step size needs to be very small. Finally, we investigate and compute the errors of the four proposed methods for different step sizes to examine superiority. Several numerical examples are given to demonstrate the reliability and efficiency.

Ordinary differential equation, initial value problem, Adams Moulton Predictor-Corrector method, RK method, Taylor’s series method, Picard’s method, Milnes method and ERROR ANALYSIS.

"COMPARISON BETWEEN SINGLE-STEP METHOD AND MULTISTEP METHOD USING TAYLOR’S SERIES METHOD MILNES METHOD PICARD’S METHOD AND ADAMS MOULTON METHOD", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 11, page no.382-388, November-2018, Available :http://www.jetir.org/papers/JETIR1811248.pdf

"COMPARISON BETWEEN SINGLE-STEP METHOD AND MULTISTEP METHOD USING TAYLOR’S SERIES METHOD MILNES METHOD PICARD’S METHOD AND ADAMS MOULTON METHOD", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 11, page no. pp382-388, November-2018, Available at : http://www.jetir.org/papers/JETIR1811248.pdf