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SageMath is designed partially as a free alternative to the general-purpose mathematics products Maple and MATLAB. It can be downloaded or used through a web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python.
Yes, BDF, Runge-Kutta (RK34, Cash-Karp 5, Dormand-Prince 5), and generalized alpha time stepping Runge-Kutta, SSP, SDIRK, Adams-Bashforth, Adams-Moulton, Symplectic Integration Algorithm, Newmark method, Generalized-alpha method Any user implemented and/or from a set of predefined. Explicit methods: forward Euler, 3rd and 4th order Runge-Kutta.
Following a redesign of the software organization, Gerris became Basilisk, [17] which allows one to develop its own solver (not necessarily in fluid mechanics) using various data structures (including of course the quadtree/octree) and optimized operators for iteration, derivation, etc. Solvers are written in C, more specifically the Basilisk C ...
MINOS is a Fortran software package for solving linear and nonlinear mathematical optimization problems. MINOS (Modular In-core Nonlinear Optimization System) may be used for linear programming, quadratic programming, and more general objective functions and constraints, and for finding a feasible point for a set of linear or nonlinear equalities and inequalities.
For solving these problems, Couenne uses a reformulation procedure [2] and provides a linear programming approximation of any nonconvex optimization problem. [ 3 ] Couenne is an implementation of a branch-and-bound where every subproblem is solved by constructing a linear programming relaxation to obtain a lower bound.
The IBM ILOG CPLEX Optimizer solves integer programming problems, very large [3] linear programming problems using either primal or dual variants of the simplex method or the barrier interior point method, convex and non-convex quadratic programming problems, and convex quadratically constrained problems (solved via second-order cone programming, or SOCP).
One can think of this method as a conservative finite volume method which solves exact, or approximate Riemann problems at each inter-cell boundary. In its basic form, Godunov's method is first order accurate in both space and time, yet can be used as a base scheme for developing higher-order methods.
God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, [1] but which can also be applied to other combinatorial puzzles and mathematical games. [2] It refers to any algorithm which produces a solution having the fewest possible moves (i.e., the solver should not require any more than this number).