Lecture

Numerical Methods: Runge-Kutta Approximation

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In course

MATH-351: Advanced numerical analysis II

The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail. ...

Description

This lecture covers the Runge-Kutta method for approximating solutions of differential equations, focusing on stages, implementation, and justification. The instructor explains the theory, formulas, and proof of order, providing insights into the computational complexity and practical applications.

Instructor

Marco Picasso

Expertise Computational Science and Engineering Mission I am teaching analysis and numerical analysis for engineers and mathematicians at bachelor and master levels.My research pertains to the numerical simulation of complex physical systems with partial differential equations.Here is some bibliometry: Google Scholar, Research Gate, Orcid, here is my most recent CV. Ongoing research projects: - Numerical simulation of aluminium electrolysis, collaboration with RioTinto LRF lab, Ycoorsystems SA and Jacques

Official source

Related concepts (32)

Y, or y, is the twenty-fifth and penultimate letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. According to some authorities, it is the sixth (or seventh if including W) vowel letter of the English alphabet. In the English writing system, it mostly represents a vowel and seldom a consonant, and in other orthographies it may represent a vowel or a consonant. Its name in English is wye (pronounced 'waɪ), plural wyes.

K, or k, is the eleventh letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is kay (pronounced 'keɪ), plural kays. The letter K usually represents the voiceless velar plosive. The letter K comes from the Greek letter Κ (kappa), which was taken from the Semitic kaph, the symbol for an open hand. This, in turn, was likely adapted by Semitic tribes who had lived in Egypt from the hieroglyph for "hand" representing /ḏ/ in the Egyptian word for hand, ⟨ḏ-r-t⟩ (likely pronounced /ˈcʼaːɾat/ in Old Egyptian).

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

H, or h, is the eighth letter in the Latin alphabet, used in the modern English alphabet, including the alphabets of other western European languages and others worldwide. Its name in English is aitch (pronounced eɪtʃ, plural aitches), or regionally haitch heɪtʃ. The original Semitic letter Heth most likely represented the voiceless pharyngeal fricative (ħ). The form of the letter probably stood for a fence or posts. The Greek Eta 'Η' in archaic Greek alphabets, before coming to represent a long vowel, /ɛː/, still represented a similar sound, the voiceless glottal fricative /h/.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

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Ordinary differential equation

Differential equation