A Weighted Scheme Of Ordinary Differential Equation In Initial Value Problem

This paper introduces weighted improvement Euler method for computing initial problem in differential equation. This method is improved through weighted forward and backward Euler-method of Euler improvement method. The method's error and its comparison with the improvement Euler method have been carried out. The results show weighted method is better than the Euler method. Some properties such as compatibility and stability & convergence etc. about weighted method have been deduced. Finally numerical experiments prove the efficiency of weighted method.