AN ITERATIVE INTEGRATION SCHEME FOR SOLVING 2ND-ORDER ORDINARY DIFFERENTIAL-EQUATIONS

This paper presents an iterative solution method for the numerical integration of second-order ordinary differential equations using a simple program for microcomputers (PC). The method of integration proposed is based on the geometrical considerations in the phase plane. The numerical results are compared to those obtained by the fourth-order Runge-Kutta method and to the closed form solutions when possible. Tests show good accuracy and, in some cases, computer time saving with respect to the Runge-Kutta's method for the same accuracy. The method of integration in the phase plane seems very good for treating every kind of nonlinear second-order differential equation whatever the degree of nonlinearity.