University Institute of Engineering and Technology, Panjab University, Chandigarh 160 014, India
In this paper, we propose a class of the backward Euler's method for the numerical solution of initial value problems of ordinary differential equations. The proposed class is constructed by considering a suitable interpolating function. The accuracy and stability of the proposed class are considered. A comparison of numerical results obtained by some of the proposed methods and the existing classical backward Euler's method is given which demonstrate that for the problems tested here the proposed methods outperform the existing classical method.
Ordinary differential equations, Initial value problems, Stability, Interpolation
