Numerical Solution of Ordinary Differential Equations and Applications
In this paper, we introduce various numerical methods for the solution of ordinary differential equations and
applications. We consider the general first order differential equation / = ( , ) with the initial condition y(x 0 ) =y 0.
We can solve the ordinary differential equations by using the following methods.
i) Taylor series Method, ii) Picard Method, iii) Euler Method, iv) Modified Euler Method & v) Runge-Kutta Method
Keywords— Ordinary Differential Equation, Analytical Method, Closed-Form Solution, Initial Condition, Step-By-Step
Methods, Marching Methods, Independent Variable, Dependent Variable, Interval, Range, Finite Differences, Starting
Values, Initial Value Problems, Boundary Value Problems.