We have recently been looking at ordinary differential equations, or ODEs, which relate the derivatives of one variable with respect to another to them with a function so that we cannot solve them with plain integration. Whilst there are a number of tricks for solving such equations if they have very specific forms, we typically have to resort to approximation algorithms such as the Euler method, with first order errors, and the midpoint method, with second order errors.

In this post we shall see that these are both examples of a general class of algorithms that can be accurate to still greater orders of magnitude.

In this post we shall see that these are both examples of a general class of algorithms that can be accurate to still greater orders of magnitude.

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