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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.
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 ...
Figure 1. Xcas calculates fractions without common denominator. Figure 2. Xcas can solve equation, calculate derivative, antiderivative and more. Figure 3. Xcas can solve differential equations. Xcas is a user interface to Giac, which is an open source [2] computer algebra system (CAS) for Windows, macOS and Linux among many other platforms.
Atangana and Kilicman extended the fractional advection dispersion equation to a variable order equation. In their work, the hydrodynamic dispersion equation was generalized using the concept of a variational order derivative. The modified equation was numerically solved via the Crank–Nicolson method.
When a partial fraction term has a single (i.e. unrepeated) binomial in the denominator, the numerator is a residue of the function defined by the input fraction. We calculate each respective numerator by (1) taking the root of the denominator (i.e. the value of x that makes the denominator zero) and (2) then substituting this root into the ...
The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.
Universal differential equation — differential–algebraic equation whose solutions can approximate any continuous function; Fekete problem — find N points on a sphere that minimize some kind of energy; Carleman's condition — condition guaranteeing that a measure is uniquely determined by its moments
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 ...