Abstract
In this chapter, we provide a survey of results concerning the computability and computational complexity of differential equations. In particular, we study the conditions which ensure computability of the solution to an initial value problem for an ordinary differential equation (ODE) and analyze the computational complexity of a computable solution. We also present computability results concerning the asymptotic behaviors of ODEs as well as several classically important partial differential equations.
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GraÇa, D.S., Zhong, N. (2021). Computability of Differential Equations. In: Brattka, V., Hertling, P. (eds) Handbook of Computability and Complexity in Analysis. Theory and Applications of Computability. Springer, Cham. https://doi.org/10.1007/978-3-030-59234-9_3
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DOI: https://doi.org/10.1007/978-3-030-59234-9_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-59233-2
Online ISBN: 978-3-030-59234-9
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