Abstract
Integral calculus provides the mathematical tools to solve differential equations; however, integration isn’t always straightforward, and even symbolic software can be challenged in routine situations. Moreover, many applications are complicated, and closed-form solutions are either impractical or impossible to compute. The methods of this chapter instead develop a class of widely used algorithms to iteratively approximate a solution.
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- 1.
We technically have that if Δt j ↓ 0 as j →∞, then there is a subsequence \(\varDelta t_{j_i}\) such that \(\eta (\varDelta _{j_i}) / \varDelta _{j_i}\) converges as i →∞. We are assuming such a subsequence for motivational purposes.
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Holder, A., Eichholz, J. (2019). Ordinary Differential Equations. In: An Introduction to Computational Science. International Series in Operations Research & Management Science, vol 278. Springer, Cham. https://doi.org/10.1007/978-3-030-15679-4_5
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DOI: https://doi.org/10.1007/978-3-030-15679-4_5
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