Existence and Uniqueness of Solutions - MATH 365 Ordinary ...
Existence and Uniqueness of Solutions - MATH 365 Ordinary ...
Existence and Uniqueness of Solutions - MATH 365 Ordinary ...
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Integral Equation (2 <strong>of</strong> 2)<br />
We have just shown that solving the initial value problem<br />
dy<br />
= f(t, y)<br />
dt<br />
y(0) = 0<br />
is equivalent to solving the integral equation<br />
φ(t) =<br />
t<br />
0<br />
f(s,φ(s)) ds.<br />
To prove the existence <strong>and</strong> uniqueness theorem it is more<br />
convenient to find a unique solution to the integral equation.<br />
The procedure for solving the integral equation is called the<br />
method <strong>of</strong> successive approximations or sometimes Picard<br />
iteration.<br />
J. Robert Buchanan <strong>Existence</strong> <strong>and</strong> <strong>Uniqueness</strong> <strong>of</strong> <strong>Solutions</strong>
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