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The Gross–Pitaevskii equation (GPE, named after Eugene P. Gross [1] and Lev Petrovich Pitaevskii [2]) describes the ground state of a quantum system of identical bosons using the Hartree–Fock approximation and the pseudopotential interaction model. A Bose–Einstein condensate (BEC) is a gas of bosons that are in the same quantum state, and ...
Cnoidal wave solution to the Korteweg–De Vries equation, in terms of the square of the Jacobi elliptic function cn (and with value of the parameter m = 0.9). Numerical solution of the KdV equation u t + uu x + δ 2 u xxx = 0 (δ = 0.022) with an initial condition u(x, 0) = cos(πx). Time evolution was done by the Zabusky–Kruskal scheme. [1]
Pseudo-spectral method. Pseudo-spectral methods, [1] also known as discrete variable representation (DVR) methods, are a class of numerical methods used in applied mathematics and scientific computing for the solution of partial differential equations. They are closely related to spectral methods, but complement the basis by an additional ...
uBLAS is a C++ template class library that provides BLAS level 1, 2, 3 functionality for dense, packed and sparse matrices. Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor is a high performance tensor (fixed multi-dimensional array) library for modern C++.
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of ...
ALGLIB is an open source numerical analysis library which may be used from C++, C#, FreePascal, Delphi, VBA. ArrayFire is a high performance open source software library for parallel computing with an easy-to-use API. IMSL Numerical Libraries are libraries of numerical analysis functionality implemented in standard programming languages like C ...
Specific potential energy. In classical mechanics and gravitational physics, massic gravitational potential energy (MGPE) is a fundamental concept that relates to the gravitational potential a body possesses due to its position in a gravitational field relative to a reference point. This energy is associated with the gravitational force acting ...
Dormand–Prince method. In numerical analysis, the Dormand–Prince (RKDP) method or DOPRI method, is an embedded method for solving ordinary differential equations (ODE). [1] The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate fourth- and fifth-order accurate ...