• C SENTHILNATHAN
• DR.S KARUNANITHI
• PROF.N.GAJALAKSHMI
• PROF.M.MALARVIZHI

So far , This paper mainly presents fourth-order of Taylor’s Method and fourth-order of Runge-kutta’s method for solving initial value problems (IVP) for ordinary differential equations (ODE). The three 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 in Matlab. The numerical solutions are in good agreement with the exact solutions. Numerical comparisons between Fourth-order Taylor’s Method and fourth-order of Runge-kutta’s method have been compare. We also compare the performance and the computational effort of such methods. In order to achieve higher accuracy in the solution, the step size needs to be very small. Finally we investigate and compute the errors of the three proposed methods for different step sizes to examine superiority.

Initial Value Problem (IVP), Fourth-Order of Taylor’s method , Fourth-Order of Runge Kutta Method, Error Analysis, MATLAB

"A Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with 4th-Order of Taylor’s Method and 4th-Order of RK Methods Using Matlab", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 4, page no.135-142, April-2018, Available :http://www.jetir.org/papers/JETIR1804028.pdf

"A Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with 4th-Order of Taylor’s Method and 4th-Order of RK Methods Using Matlab", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 4, page no. pp135-142, April-2018, Available at : http://www.jetir.org/papers/JETIR1804028.pdf