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GUI operation is recorded as equivalent function calls, and therefore in addition to binary formats, FEATool simulation models can also be saved and exported as fully scriptable and editable MATLAB compatible m-script files. [13] The short MATLAB script below illustrates how a complete flow around a cylinder computational fluid dynamics (CFD ...
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 (+) + (() +).
MODFLOW simulation. MODFLOW is the U.S. Geological Survey modular finite-difference flow model, which is a computer code that solves the groundwater flow equation.The program is used by hydrogeologists to simulate the flow of groundwater through aquifers.
Its text-based programming language MathScript uses .m-file-script syntax providing some compatibility with MATLAB and its clones. LAPACK provides Fortran 90 routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems and the associated ...
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
The classical Pade scheme for the first derivative at a cell with index (′) reads; ′ + ′ + + ′ = +. Where is the spacing between points with index , & +.The equation yields a fourth-order accurate solution for ′ when supplemented with suitable boundary conditions (typically periodic).
The discrete difference equations may then be solved iteratively to calculate a price for the option. [4] The approach arises since the evolution of the option value can be modelled via a partial differential equation (PDE), as a function of (at least) time and price of underlying; see for example the Black–Scholes PDE. Once in this form, a ...