December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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6.4 Higher-Order Equations and Systems
INTRODUCTION
So far we have focused on numerical techniques that can be used to approximate the solution of a first-order initial-value problem y′ = f(x, y), y(x0) = y0. In order to approximate the solution of a second-order initial-value problem we must express a second-order DE as a system of two first-order DEs. To do this we begin by writing the second-order DE in normal form by solving for y″ in terms of x, y, and y′.
Second-Order IVPs
A second-order initial-value problem
y″ = f(x, y, y′), y(x0) = y0, y′(x0) = u0,(1)
can be expressed as an initial-value problem for a system of first-order differential ...
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