What is quasilinear equation?
Quasilinear equation, a type of differential equation where the coefficient(s) of the highest order derivative(s) of the unknown function do not depend on highest order derivative(s) …
What is an Indicial equation?
An indicial equation is one in which the power is the unknown, e.g. 2n = 8 the solution of which would be n = 3. Indicial equations often occur in the calculation of compound interest.
What is order differential equation?
The order of a differential equation is defined to be that of the highest order derivative it contains. The degree of a differential equation is defined as the power to which the highest order derivative is raised. The equation (f‴)2 + (f″)4 + f = x is an example of a second-degree, third-order differential equation.
How do you know if a function is quasilinear?
Definition in terms of preferences In other words: a preference relation is quasilinear if there is one commodity, called the numeraire, which shifts the indifference curves outward as consumption of it increases, without changing their slope.
What is Indicial equation in Ode?
The general definition of the indicial polynomial is the coefficient of the lowest power of z in the infinite series. In this case it happens to be that this is the rth coefficient but, it is possible for the lowest possible exponent to be r − 2, r − 1 or, something else depending on the given differential equation.
What does Indicial mean?
Definition of indicial 1 : of, relating to, or having the nature of an indication : indicative a remark indicial of their pride. 2 [Latin indic-, index index finger, index + English -ial] a : of, relating to, or having the nature of an index an indicial glossary. b : of or relating to the index finger.
What is a differential in maths?
differential, in mathematics, an expression based on the derivative of a function, useful for approximating certain values of the function. The derivative of a function at the point x0, written as f′(x0), is defined as the limit as Δx approaches 0 of the quotient Δy/Δx, in which Δy is f(x0 + Δx) − f(x0).
What is arbitrary constant in differential equation?
An arbitrary constant is a constant whose value could be assumed to be anything, just so long as it doesn’t depend on the other variables in an equation or expression. A constant that’s not arbitrary can usually just take one value (or perhaps, a set of possible values, but not just any value).
What do quasilinear preferences mean?
When is a partial differential equation said to be quasilinear?
Definition 3: A partial differential equation is said to be quasilinear if it is linear with respect to all the highest order derivatives of the unknown function. What does mean to be linear with respect to all the highest order derivatives?
Which is the basic method for investigating quasilinear equations?
Ever since the first fundamental paper t1] was published on the theory of generalized solutions of quasilinear equations, the basic method for investigating these equations has remained the “vanishing viscosity method,” which is based on the idea of passing to the limit as ( > + 0 in the parabolic equation
What is the meaning of quasilinear in PDE?
To understand the meaning of quasilinear, it is helpful to start with the first-order case. On reference.wolfram.com, quasilinear is defined as follows: where a, b and c can be nonlinear functions. For higher order equations, we can have nonlinear functions of some of the derivates, so long as they are not the highest order.
Can a quasilinear equation have a second order derivative?
If you have a second order derivative, it does not matter if the equation has a term like u 2 to be quasilinear. You just need to check the highest order derivatives (second order ones in the examples of the link). To understand the meaning of quasilinear, it is helpful to start with the first-order case.