Search results
Results from the WOW.Com Content Network
FEATool Multiphysics is a fully integrated physics and PDE simulation environment where the modeling process is subdivided into six steps; preprocessing (CAD and geometry modeling), mesh and grid generation, physics and PDE specification, boundary condition specification, solution, and postprocessing and visualization.
Full API for Java and, through add-on product, Matlab Runtime parsed mathematical expression in input files Fully scriptable in as m-file Matlab scripts and the GUI supports exporting models in script format automatic differentiation: Yes Yes Yes Forward-mode for Jacobian computation, symbolic differentiation capabilities multiphysics:
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).
APMonitor: APMonitor is a mathematical modeling language for describing and solving representations of physical systems in the form of differential and algebraic equations. Armadillo is C++ template library for linear algebra; includes various decompositions, factorisations, and statistics functions; its syntax is similar to MATLAB.
Other books on similar topics include A Treatise on the Calculus of Finite Differences by George Boole, Introduction to Difference Equations by S. Goldberg, [5] Difference Equations: An Introduction with Applications by W. G. Kelley and A. C. Peterson, An Introduction to Difference Equations by S. Elaydi, Theory of Difference Equations: An Introduction by V. Lakshmikantham and D. Trigiante ...
The slope field can be defined for the following type of differential equations y ′ = f ( x , y ) , {\displaystyle y'=f(x,y),} which can be interpreted geometrically as giving the slope of the tangent to the graph of the differential equation's solution ( integral curve ) at each point ( x , y ) as a function of the point coordinates.
A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. [1] [2] The order of the equation is the maximum time gap between any two indicated values of the variable vector. For ...
In numerical analysis and computational fluid dynamics, Godunov's scheme is a conservative numerical scheme, suggested by Sergei Godunov in 1959, [1] for solving partial differential equations. 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 ...