Explicit and implicit methodsExplicit and implicit methods are approaches used in numerical analysis for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes. Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while implicit methods find a solution by solving an equation involving both the current state of the system and the later one.
Finite difference methodIn numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
Chicken (Scheme implementation)Chicken (stylized as CHICKEN) is a programming language, specifically a compiler and interpreter which implement a dialect of the programming language Scheme, and which compiles Scheme source code to standard C. It is mostly R5RS compliant and offers many extensions to the standard. The newer R7RS standard is supported through an extension library. Chicken is free and open-source software available under a BSD license. It is implemented mostly in Scheme, with some parts in C for performance or to make embedding into C programs easier.
Numerical methods for ordinary differential equationsNumerical 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.
Data integrationData integration involves combining data residing in different sources and providing users with a unified view of them. This process becomes significant in a variety of situations, which include both commercial (such as when two similar companies need to merge their databases) and scientific (combining research results from different bioinformatics repositories, for example) domains. Data integration appears with increasing frequency as the volume (that is, big data) and the need to share existing data explodes.
Enterprise integrationEnterprise integration is a technical field of enterprise architecture, which is focused on the study of topics such as system interconnection, electronic data interchange, product data exchange and distributed computing environments. It is a concept in enterprise engineering to provide the relevant information and thereby enable communication between people, machines and computers and their efficient co-operation and co-ordination.
Scheme (programming language)Scheme is a dialect of the Lisp family of programming languages. Scheme was created during the 1970s at the MIT Computer Science and Artificial Intelligence Laboratory (MIT AI Lab) and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers. It was the first dialect of Lisp to choose lexical scope and the first to require implementations to perform tail-call optimization, giving stronger support for functional programming and associated techniques such as recursive algorithms.
Python (programming language)Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library.
Ruby (programming language)Ruby is an interpreted, high-level, general-purpose programming language which supports multiple programming paradigms. It was designed with an emphasis on programming productivity and simplicity. In Ruby, everything is an object, including primitive data types. It was developed in the mid-1990s by Yukihiro "Matz" Matsumoto in Japan. Ruby is dynamically typed and uses garbage collection and just-in-time compilation. It supports multiple programming paradigms, including procedural, object-oriented, and functional programming.
Sparse matrixIn numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.
Chromium (web browser)Chromium is a free and open-source web browser project, mainly developed and maintained by Google. This codebase provides the vast majority of code for the Google Chrome browser, which is proprietary software and has some additional features. Chromium's logo is identical in shape to that of Google Chrome, but with blue colors instead of being multicolor. The Chromium codebase is widely used. Microsoft Edge, Samsung Internet, Opera, and many other browsers are based on the Chromium code.
Web browserA web browser is an application for accessing websites. When a user requests a web page from a particular website, the browser retrieves its from a web server and then displays the page on the user's screen. Browsers are used on a range of devices, including desktops, laptops, tablets, and smartphones. In 2020, an estimated 4.9 billion people have used a browser. The most used browser is Google Chrome, with a 65% global market share on all devices, followed by Safari with 18%.
Opera (web browser)Opera is a multi-platform web browser developed by its namesake company Opera. The browser is based on Chromium, but distinguishes itself from other Chromium-based browsers (Chrome, Edge, etc.) through its user interface and other features. Opera was initially released on 10 April 1995, making it one of the oldest desktop web browsers still actively developed. It was commercial software for its first ten years and had its own proprietary layout engine, Presto. In 2013, it switched from the Presto engine to Chromium.
Browser engineA browser engine (also known as a layout engine or rendering engine) is a core software component of every major web browser. The primary job of a browser engine is to transform HTML documents and other resources of a web page into an interactive visual representation on a user's device. A browser engine is not a stand-alone computer program but a critical piece of a more extensive program, such as a web browser, from which the term is derived. The word "engine" is an analogy to the engine of a car.
Browser extensionA browser extension is a software module for customizing a web browser. Browsers typically allow users to install a variety of extensions, including user interface modifications, cookie management, ad blocking, and the custom scripting and styling of web pages. Browser plug-ins are a different type of module and no longer supported by the major browsers. One difference is that extensions are distributed as source code, while plug-ins are executables (i.e. object code).
Newmark-beta methodThe Newmark-beta method is a method of numerical integration used to solve certain differential equations. It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems. The method is named after Nathan M. Newmark, former Professor of Civil Engineering at the University of Illinois at Urbana–Champaign, who developed it in 1959 for use in structural dynamics.
Finite element machineThe Finite Element Machine (FEM) was a late 1970s-early 1980s NASA project to build and evaluate the performance of a parallel computer for structural analysis. The FEM was completed and successfully tested at the NASA Langley Research Center in Hampton, Virginia. The motivation for FEM arose from the merger of two concepts: the finite element method of structural analysis and the introduction of relatively low-cost microprocessors.
Seismic analysisSeismic analysis is a subset of structural analysis and is the calculation of the response of a building (or nonbuilding) structure to earthquakes. It is part of the process of structural design, earthquake engineering or structural assessment and retrofit (see structural engineering) in regions where earthquakes are prevalent. As seen in the figure, a building has the potential to 'wave' back and forth during an earthquake (or even a severe wind storm). This is called the 'fundamental mode', and is the lowest frequency of building response.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
Numerical stabilityIn 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.
