Hamiltonian Mechanics and the Construction of Numerical Integrators
نویسنده
چکیده
Introductory courses on differential equations cover integration techniques for integrable differential equations. However, most systems of ordinary differential equations are too complicated to be integrated exactly. Therefore, mathematicians have developed ways through which we can approximate such systems. These numerical integrators solve systems of differential equations to within a certain error. The complexity and cost of such integrators grows with their precision. Numerical analysts are always looking for new integration schemes that have low error and low cost. In this paper, we discuss the derivation of numerical integrators as well as their benefits and disadvantages.
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