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.
Runge–Kutta methodsIn numerical analysis, the Runge–Kutta methods (ˈrʊŋəˈkʊtɑː ) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta. The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
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.
Luxury goodsIn economics, a luxury good (or upmarket good) is a good for which demand increases more than what is proportional as income rises, so that expenditures on the good become a greater proportion of overall spending. Luxury goods are in contrast to necessity goods, where demand increases proportionally less than income. Luxury goods is often used synonymously with superior goods. The word "luxury" derives from the Latin verb luxor meaning to overextend or strain.
Production planningProduction planning is the planning of production and manufacturing modules in a company or industry. It utilizes the resource allocation of activities of employees, materials and production capacity, in order to serve different customers. Different types of production methods, such as single item manufacturing, batch production, mass production, continuous production etc. have their own type of production planning. Production planning can be combined with production control into production planning and control, or it can be combined with enterprise resource planning.
Luxury carA luxury car is a car that provides above-average to high-end levels of comfort, features, and equipment. Often more expensive materials and surface finishes are used, and buyers expect better build quality. The usually higher pricing and more upscale appearance is often associated with higher social status of the users, compared to low and mid-market segment cars. The term is relative and partially subjective, reflecting both objective qualities of a car, as well as the projected and perceived of the car marque.
Louis VuittonLouis Vuitton Malletier, commonly known as Louis Vuitton (luːˈiː_vɪˈtɒn, lwi vɥitɔ̃), is a French luxury fashion house and company founded in 1854 by Louis Vuitton. The label's LV monogram appears on most of its products, ranging from luxury bags and leather goods to ready-to-wear, shoes, perfumes, watches, jewellery, accessories, sunglasses and books. Louis Vuitton is one of the world's leading international fashion houses. It sells its products through standalone boutiques, lease departments in high-end departmental stores, and through the e-commerce section of its website.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
