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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 (+) + (() +).
Thus it cannot be used directly on purely elliptic partial differential equations, such as Laplace's equation. However, MOL has been used to solve Laplace's equation by using the method of false transients. [1] [8] In this method, a time derivative of the dependent variable is added to Laplace’s equation. Finite differences are then used to ...
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.
Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation. The method is to reduce a partial differential equation (PDE) to a family of ordinary differential equations (ODE) along which the solution can be integrated from some initial data ...
The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.
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.
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable.As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. [1]