Methods Of Solution To Non-Linear Ordinary Differential Equations.

ABSTRACT

Differential equations were classified as Linear and non-Linear. It was noted that most real life problems when handled by mathematical formulation take the form of Non- Linear differential - equation. This non-Linear differential equation can be partial or ordinary. In particular, we considered the methods of solution to the ordinary types because an understanding of the solution methods of this is good enough to provide solution to the partial forms. This is because the partial forms can easily be reduced to ordinary forms by transformation. Since analytical solution to most non-linear ordinary differential equation is almost impossible analytically studied here the possible methods available, namely, the pertuhations, Numerical and the Laplace transforms. We equally looked at the inefficiencies of or difficulties in using any of the methods becuase of the availability of computers, it is now very possible to provide solutions to our problems using numerical methods. There are good software packages that can efficiently handle numerical problems. Some of the key symbols used are

i. = epsilon

ii L = Laplace transform

iii. L = Inverse laplace transform

iv. a = Alfa

v. = Beta