SUMMARY
In chapter one, differential equation was introduced, this includes a brief history of differential equations, types of differential equations that is, the ordinary differential equation and the partial differential equation. The essence of solving differential equations was also discussed as well as some analytical methods of solving these equations.
The numerical methods such as the one step methods which includes the Euler method and the Runge kutta method was discussed in chapter two of this study. The Linear Multistep method was also analysed and method like the Adam’s implicit and Explicit methods, Backward differentiation formula and some basic definitions were given.
The proposed method was discussed in chapter three, which is the modification of the backward differential formula by adding a previous point and introducing a constant. The coefficients of the new method with the aid of MATHEMATICA were generated for each k step.
The stability of the method developed in chapter three was examined in chapter four. The stability region and order and error constants were also determined.
The further research will be to implement this method to investigate stiff ordinary differential equations.
