Ordinary Differential Equations

Clemens Heitzinger ()
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Clemens Heitzinger: Technische Universität Wien, Center for Artificial Intelligence and Machine Learning (CAIML) and Department of Mathematics and Geoinformation

Chapter Chapter 9 in Algorithms with JULIA, 2022, pp 229-256 from Springer

Abstract: Abstract Differential equations are among the most successful models in physics, chemistry, biology, engineering, and many other fields. This chapter is concerned with solving systems of ordinary differential equations. Ordinary differential equations are equations that contain derivatives with respect to only one independent variable. The main result that a system of ordinary differential equations has a unique solution under certain reasonable assumptions is presented. In order to solve the equations numerically, runge–kutta formulas are discussed in detail, since they yield excellent results for a wide range of equation types. Finally, the formulas are implemented in an idiomatic manner in julia.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-16560-3_9

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DOI: 10.1007/978-3-031-16560-3_9

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