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Improvements on the Euler Method

We have seen that the Euler method is not sufficiently accurate to be an efficient problem-solving procedure, so it is desirable to develop more accurate methods. Consider the initial value problem

and let denote its solution. By integrating the given differential equation from to we obtain

 

The Euler formula

is obtained by replacing in eq. (11) by its approximate value at the left endpoint of the interval of intergration.





Dinesh Manocha
Sun Mar 15 12:31:03 EST 1998