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Numerical integration of ODE’s with Automatic differentiation

Levi, Nadav (2021) Numerical integration of ODE’s with Automatic differentiation. Bachelor's Thesis, Mathematics.

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Abstract

In this bachelor project we will look at solving Initial Value Problems of Ordi- nary Differential Equations by means of numerical integration. Namely, we will be looking at the Taylor method, which approximates a solution of an ODE by using the Taylor series expansion of the function on various points on a grid. One of the main drawbacks of the Taylor method is the need to compute higher order deriva- tives, which can be computationally expensive as the number of terms grow expo- nentially. To this end, we present the method of Automatic Differentiation, which is a recursive procedure of generating high-order derivatives. Automatic differenti- ation bypasses the inefficiency of Symbolic Differentiation and the shortcomings of Numerical Differentiation with respect to round-off and truncation errors. Lastly, we will use the method to evaluate a number of problems from classical mechanics and compare the results to other numerical integrators such as Runge-Kutta.

Item Type: Thesis (Bachelor's Thesis)
Supervisor name: Seri, M. and Jardon Kojakhmetov, H.
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 20 Jul 2021 13:11
Last Modified: 20 Jul 2021 13:11
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/25354

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