Summary: DIFFERENTIAL EQUATIONS
A principal model of physical phenomena.
The equation:
y0 = f(x; y)
The initial value:
y(x0) = Y0
Find solution Y (x) on some interval x0 x b: To-
gether these two conditions constitute an initial value
problem.
We will study methods for solving systems of rst or-
der equations, but we begin with a single equation.
Many of the crucial ideas in the numerical analysis
arise from properties of the original equation.
SPECIAL CASES
1. y0(x) = y(x) + b(x); x x0;
f(x; z) = z + b(x).
General solution:
Y (x) = ce x +
Z x
x0

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

Collections: Computer Technologies and Information Sciences