Page 212 - Schaum's Outline of Differential Equations

CHAPTER 20

Numerical Methods for

Solving Second-Order

Differential Equations

Via Systems

SECOND-ORDER DIFFERENTIAL EQUATIONS

In Chapter 17. we showed how a second (or higher)-order differeiilial equation could he expressed as a
system of first-order differential equations.
In this chapter we investigate several numerical techniques dealing with such sjslems.
In the following s\stem of initial-value problems, v and .: are functions of x,

We note that. w'\thy'=f(x,y,z) = z. System (20./) represenls ihe second-order initial-value problem

Standard form for a svslcm of three equations is

1
i
If. in such a system, /(.v, v, c, vt ) = ;. and g(x, v, ;, w) = vv. ihcn sjslem (20.2) represents ihu ihird-ordcr nitial-
value problem

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