THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS BY THE TAYLOR-SERIES METHOD

摘要

The Taylor series method [1] has long been regarded as an efficient procedure for solving systems of ordinary differential equations. Frequently, it is necessary to algebraically manipulate the differential system into an equivalent system. The Taylor coefficients for this modi¬fied system may be simply written. However, the required modification is a tedious and error prone task for all but the simplest systems. For this reason, the Taylor series method has often been excluded by numerical analysts from consideration as a general purpose integrator.