Lecture

Numerical Methods: Order of Accuracy

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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 concept of order of accuracy in numerical methods, focusing on schemes of different orders and their error analysis. The instructor explains how to choose parameters to achieve a desired level of accuracy and discusses the implications of the order of accuracy on the final results.

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

Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Related concepts (31)

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

Lexicographic order

In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.

Order (mathematics)

Order in mathematics may refer to: Total order and partial order, a binary relation generalizing the usual ordering of numbers and of words in a dictionary Ordered set Order in Ramsey theory, uniform structures in consequence to critical set cardinality Order (group theory), the cardinality of a group or period of an element Order of a polynomial (disambiguation) Order of a square matrix, its dimension Order (ring theory), an algebraic structure Ordered group Ordered field Order (differential equation) or or

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.

Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection.

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