ABSTRACT
Given a system of initial value problems for ordinary differential equations, the method is to replace each dependent variable present by a Taylor series centered at a certain origin. The coefficients in each Taylor series are regarded as unknown quantities. The ordinary differential equations are used to obtain a set of recurrence relations from which the unknown coefficients may be calculated. If the Taylor series of a function is known at a single point, then the Taylor series of that function may be found at another point. This chapter illustrates the procedure on the general second order linear ordinary differential equation. The correct initial conditions for a boundary value problem can be determined by successive approximation.
