A novel algorithm using Differential Evolution techniques has been developed and applied to the solution of two-point boundary value problems for ordinary differential equations. The algorithm solves equations by discretizing the differential equation by finite-difference approximations and using differential evolution to find the set of function values that minimizes the error. The algorithm is inherently parallel, has excellent convergence properties, and is capable of solving both linear and nonlinear equations. By means of numerical experiments, the application of differential evolution to the solution of ordinary differential equations is presented as a radically different but efficient way of approaching numerical simulations, and is of importance to many disciplines.