Last time we saw how we can use Euler's method to approximate the solutions of ordinary differential equations, or ODEs, which define the derivative of one variable with respect to another as a function of them both, so that they cannot be solved by direct integration. Specifically, it uses Taylor's theorem to estimate the change in the first variable that results from a small step in the second, iteratively accumulating the results for steps of a constant length to approximate the value of the former at some particular value of the latter.

Unfortunately it isn't very accurate, yielding an accumulated error proportional to the step length, and so this time we shall take a look at a way to improve it.

Unfortunately it isn't very accurate, yielding an accumulated error proportional to the step length, and so this time we shall take a look at a way to improve it.

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