COMPUTER SYMBOLIC SOLUTION OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH ARBITRARY BOUNDARY CONDITIONS BY THE TAYLOR SERIES

Abstract

This chapter discusses the computer symbolic solution of nonlinear ordinary differential equations with arbitrary boundary conditions by Taylor series. Many theoretical tools are available for obtaining qualitative properties of the solutions of differential equations, such as solution existence over an interval of the independent variable, periodicity, quasi-periodicity, and boundedness. However, these same tools have seldom been used in actually exhibiting the analytic solution or an analytic approximation of the solution. The Taylor expansion power series can be generated by polynomial manipulation so that the size of expressions do not grow so rapidly. The computer can perform these manipulations readily. The analytical mathematical use of the digital computer is well established. There have been a number of studies dealing with the automatic computer generated analytic solution of ordinary differential equations.