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In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different ...
The facial motor nucleus contains ventral and dorsal areas that have lower motor neurons that supply the upper and lower face muscles. When central facial palsy occurs, there are lesions in the corticobulbar tract between the cerebral cortex. Because of these lesions, the facial motor nucleus reduces or destroys input in the ventral division. [1]
Facial weakness is a medical sign associated with a variety of medical conditions. [ 1 ] Some specific conditions associated with facial weakness include: [ citation needed ]
Facial nerve paralysis is a common problem that involves the paralysis of any structures innervated by the facial nerve.The pathway of the facial nerve is long and relatively convoluted, so there are a number of causes that may result in facial nerve paralysis. [2]
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 (+) + (() +).
Once the facial paralysis sets in, many people may mistake it as a symptom of a stroke; however, there are a few subtle differences. A stroke will usually cause a few additional symptoms, such as numbness or weakness in the arms and legs. And unlike Bell's palsy, a stroke will usually let patients control the upper part of their faces.
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.
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...