mathematics

John C. Butcher

John C. Butcher is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand John C. Butcher rather than just read about it. In short: John Charles Butcher (born 31 March 1933) is a New Zealand mathematician who specialises in numerical methods for the solution of ordinary differential equations. Butcher works on multistage methods for initial value problems, such as Runge-Kutta and general linear methods.

Key takeaways

John C. Butcher belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect John C. Butcher to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of John C. Butcher from memory before moving on to harder problems.

Reference excerpt

John Charles Butcher (born 31 March 1933) is a New Zealand mathematician who specialises in numerical methods for the solution of ordinary differential equations. Butcher works on multistage methods for initial value problems, such as Runge-Kutta and general linear methods. The Butcher group and the Butcher tableau are named after him. More recently, he is investigating a new type of method with stability identical to that of a Runge-Kutta method.

Biography

Butcher studied mathematics at Auckland University College - BSc and MSc - and the University of Sydney - PhD (1961) and DSc. Positions held are as aside. He was awarded the Jones Medal from the Royal Society of New Zealand in 2010, for his "exceptional lifetime work on numerical methods for the solution of differential equations and leadership in the development of New Zealand mathematical sciences." In 2011, he received the Van Wijngaarden Award. In the 2013 Queen's Birthday Honours, Butcher was appointed an Officer of the New Zealand Order of Merit, for services to mathematics.

Publications Butcher, J. C. (1975), "A stability property of implicit Runge-Kutta methods", BIT, 15 (4): 358–361, doi:10.1007/bf01931672. Butcher, John C. (2008), Numerical methods for ordinary differential equations (2nd ed.), John Wiley & Sons Ltd., doi:10.1002/9780470753767, ISBN 978-0-470-72335-7, MR 2401398. John C. Butcher: "Trees, B-series and exponential integrators", IMA Journal of Numerical Analysis Vol.30, No. 1 (Jan. 2010), pp. 131–140. DOI:10.1093/imanum/drn086. Butcher, John C. (2016), Numerical methods for ordinary differential equations (3rd ed.), John Wiley & Sons Ltd., doi:10.1002/9781119121534, ISBN 978-1-119-12150-3. J.C.Butcher:"Trees and B-series", Numerical Algorithms (2019), vol.81, pp. 1311–1325. https://doi.org/10.1007/s11075-018-0643-7 John C. Butcher: "B-Series : Algebraic Analysis of Numerical Methods", Springer(SSCM, volume 55), ISBN 978-3030709556 (April, 2021).

References

External links

Auckland Home page Personal Home page Homepage of John C. Butcher John C. Butcher at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with John C. Butcher

Start with the simplest possible case. Write down what John C. Butcher claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to John C. Butcher before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about John C. Butcher ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of John C. Butcher

In research: John C. Butcher appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses John C. Butcher in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: John C. Butcher is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1933 births, 20th-century New Zealand mathematicians, 21st-century New Zealand mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John C. Butcher outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study John C. Butcher in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what John C. Butcher means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain John C. Butcher out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is John C. Butcher in simple terms?

Why does John C. Butcher matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study John C. Butcher?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on John C. Butcher.