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.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
ToolA tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates back hundreds of millennia, have been observed using tools to make other tools. Early human tools, made of such materials as stone, bone, and wood, were used for the preparation of food, hunting, the manufacture of weapons, and the working of materials to produce clothing and useful artifacts and crafts such as pottery, along with the construction of housing, businesses, infrastructure, and transportation.
Hand toolA hand tool is any tool that is powered by hand rather than a motor. Categories of hand tools include wrenches, pliers, cutters, , striking tools, struck or hammered tools, screwdrivers, vises, clamps, snips, hacksaws, drills, and knives. Outdoor tools such as garden forks, pruning shears, and rakes are additional forms of hand tools. Portable power tools are not hand tools. Hand tools have been used by humans since the Stone Age when stone tools were used for hammering and cutting.
Verlet integrationVerlet integration (vɛʁˈlɛ) is a numerical method used to integrate Newton's equations of motion. It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics. The algorithm was first used in 1791 by Jean Baptiste Delambre and has been rediscovered many times since then, most recently by Loup Verlet in the 1960s for use in molecular dynamics. It was also used by P. H. Cowell and A. C. C.
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