Numerical Methods for Partial Differential Equations. An Introduction
1Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …
2numerical analysis — the branch of mathematics dealing with methods for obtaining approximate numerical solutions of mathematical problems. [1925 30] * * * Branch of applied mathematics that studies methods for solving complicated equations using arithmetic… …
3Numerical weather prediction — Weather models use systems of differential equations based on the laws of …
4Numerical relativity — is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end, supercomputers are often employed to study black holes, gravitational waves, neutron stars and many other… …
5Numerical integration — consists of finding numerical approximations for the value S In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also… …
6Numerical continuation — is a method of computing approximate solutions of a system of parameterized nonlinear equations, The parameter λ is usually a real scalar, and the solution an n vector. For a fixed parameter value λ,, maps Euclidean n space into itself. Often the …
7Runge–Kutta methods — In numerical analysis, the Runge–Kutta methods (pronounced IPA|/ˌʀuŋgeˈkuta/) are an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations. These techniques were… …
8Numerical analysis — Babylonian clay tablet BC 7289 (c. 1800–1600 BC) with annotations. The approximation of the square root of 2 is four sexagesimal figures, which is about six decimal figures. 1 + 24/60 + 51/602 + 10/603 = 1.41421296...[1] Numerical analysis is the …
9Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …
10Monte Carlo methods for electron transport — The Monte Carlo method for electron transport is a semiclassical Monte Carlo(MC) approach of modeling semiconductor transport. Assuming the carrier motion consists of free flights interrupted by scattering mechanisms, a computer is utilized to… …
