A new numerical method by revised measure theory for solving the nonlinear initial value problems

In this paper, we introduce a new technique to find the approximate solution of a nonlinear initial value problem (IVP). By introducing an artificial zero cost function and a linear functional, the problem is modified into one consisting of the minimization of a positive linear functional over a set of Radon measures. Then we obtain an optimal measure which is approximated by a finite combination of atomic measures, and by using atomic measures we change this one to an finite dimensional linear programming problem. Finally we find the approximated trajectory functions. Some examples are given show the procedure.