Solution of nonlinear dynamic differential equations based on numerical Laplace transform inversion

In the present paper, the dynamical differential equations with initial conditions is converted into the model of linear operator action, in which the linear operator is just the infinitesimal generator of the solver of the differential equations. And the resolvent of the linear operator is the Laplace transform of the solver of original differential equations. So the solver of original differential equations can be obtained by inversing the Laplace transform of its resolvent. An iterative algorithm for nonlinear differential equations with initial condition is easily presented by means of numerical Laplace transform inversion. The numerical examples show that the method of this paper is effective.