The Analysis or a Certain Class or Nonlinear Time-Varying Differential Equations

In this paper the partitioning technique is applied to analyze a certain class of nonlinear physical systems whose dynamic behavior can be represented by a nonlinear differential equation having some linear time-varying terms, some nonlinear terms, and a forcing function. Also included here will be some applications to specific nonlinear differential equations. It was found that by placing certain restrictions on the system equations, a unique solution could be obtained which belongs to an L
2
space. See Appendix I for an explanation of the L
2
space. This solution is given as the sequence of Pickard's iterates, each of which is also an L
2
function. In this paper, the well-known mean square error criterion is applied to find the number of iterates necessary to approximate the solution of this class of nonlinear equations.