Local Truncation Error
+O(h) h2 2 +O(h3) = y(t n)+y0(t n)h+(y0(t n+1) y0(t n)) h 2 +O(h3)+O(h3) = y(t n)+ h 2 (y 0(t n)+y(t n+1))+O(h3) Finally, since y0(t) = f(t;y(t)), we have y(t n+1) = y(t n)+ h 2 (f(t n;y(t n))+f(t n+1;y(t n+1)))+ O(h3) (1) from which we get the Trapezoidal method. The terms on the right-hand side, other than the O(h3) term, are what you would ...
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