A modified numerov integration method for general second order initial value Problems

Abstract

We present an implicit eighth-order finite difference method for the general second order non-linear differential equation Yⁿ=f(t,y,y) subject to the initial conditions y(t_o) =y_o, y(t_o)=y_O. The method is based on mixed interpolation containing a parameter which can be used to improve the accuracy. The same technique gives rise to an explicit sixth-order integration scheme. Numerical solutions of problems are given to illustrate both methods.

Keywords:

• Numerov method
• non-linear second order initial value problems

C.R. Categories:

• G.1.7
• G.1.0

^∗Research Director at the National Fund for Scientific Research (N.F.W.O. Belgium).

^∗Research Director at the National Fund for Scientific Research (N.F.W.O. Belgium).

Notes

^∗Research Director at the National Fund for Scientific Research (N.F.W.O. Belgium).