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Lecture

Implicit Euler Scheme

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 Implicit Euler Scheme, a numerical method for solving ordinary differential equations. The instructor explains the algorithm step by step, highlighting its stability and convergence properties. Through examples and derivations, the lecture demonstrates how the Implicit Euler Scheme can be applied to various differential equations.

Instructor

Marco Picasso

Official source

Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Related concepts (31)

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Detroit

Detroit (dɪˈtrɔɪt , ˈdiːtrɔɪt) is the most populous city in the U.S. state of Michigan. It is the most populous U.S. city on the United States–Canada border, and the seat of government of Wayne County. Detroit had a population of 639,111 at the 2020 census, making it the 27th-most populous city in the United States. The metropolitan area, known as Metro Detroit, is home to 4.3 million people, making it the second-largest in the Midwest after the Chicago metropolitan area, and the 14th-largest metropolitan area in the nation.

Metro Detroit

Metro Detroit is a major metropolitan area in the U.S. state of Michigan, consisting of the city of Detroit and over 200 municipalities in the surrounding area with its largest employer being Oakland County. There are varied definitions of the area, including the official statistical areas designated by the Office of Management and Budget, a federal agency of the United States. Metro Detroit is known for its automotive heritage, arts, entertainment, popular music, food, cultural diversity, and sports.

Detroit bankruptcy

The city of Detroit, Michigan, filed for Chapter 9 bankruptcy on July 18, 2013. It is the largest municipal bankruptcy filing in U.S. history by debt, estimated at

18–20 billion, exceeding Jefferson County, Alabama's

4-billion filing in 2011. Detroit is also the largest city by population in U.S. history to file for Chapter 9 bankruptcy, more than twice as large as Stockton, California, which filed in 2012. While Detroit's population had declined from a peak of 1.

History of Detroit

Detroit, the largest city in the state of Michigan, was settled in 1701 by French colonists. It is the first European settlement above tidewater in North America., p. 56. Founded as a New France fur trading post, it began to expand during the 19th century with American settlement around the Great Lakes. By 1920, based on the booming auto industry and immigration, it became a world-class industrial powerhouse and the fourth-largest city in the United States. It held that standing through the mid-20th century.

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