Indicial equation

How do you find the Indicial equation?

a(2r(r-1) + r) = 0 => r(2r-1) = 0, an equation which is called the indicial equation. The roots of this equation, r1 = 1/2 and r2 = 0, are called the exponents of the equation. You use each of these to write the recurrence relations in terms of n only.

How do you use the Frobenius method?

The method is called the Frobenius method, named after the mathematician Ferdinand Georg Frobenius. x2y + P xy + Qy = 0, (5) has a singular point at x = 0, and we know that a solution for x > 0 is given by y(x) = xr = er log x, (6) where r is a root of the characteristic (or auxiliary) equation r2 + (P − 1)r + Q = 0.

What is singular equation?

From Wikipedia, the free encyclopedia. A singular solution ys(x) of an ordinary differential equation is a solution that is singular or one for which the initial value problem (also called the Cauchy problem by some authors) fails to have a unique solution at some point on the solution.

What is Bessel differential equation?

The Bessel differential equation is the linear second-order ordinary differential equation given by. (1) Equivalently, dividing through by , (2) The solutions to this equation define the Bessel functions and .

What is a singular point in differential equations?

Consider a second-order ordinary differential equation. If and remain finite at , then is called an ordinary point. If either or diverges as , then is called a singular point. If either or diverges as but and remain finite as , then. is called a regular singular point (or nonessential singularity).

What is Legendre differential equation?

Since the Legendre differential equation is a second-order ordinary differential equation, it has two linearly independent solutions. A solution which is regular at finite points is called a Legendre function of the first kind, while a solution which is singular at is called a Legendre function of the second kind.

Why is Frobenius method used?

The Frobenius method enables one to create a power series solution to such a differential equation, provided that p(z) and q(z) are themselves analytic at 0 or, being analytic elsewhere, both their limits at 0 exist (and are finite).

How do you find singular points?

Singular points occur when a coefficient in a particular differential equation becomes unbounded. the singular points occur where Q(x)/P(x) and/or R(x)/P(x) become unbounded.

What is clairaut’s equation of differential equation?

Clairaut’s equation, in mathematics, a differential equation of the form y = x (dy/dx) + f(dy/dx) where f(dy/dx) is a function of dy/dx only. The equation is named for the 18th-century French mathematician and physicist Alexis-Claude Clairaut, who devised it.

What is singular matrix?

A square matrix that does not have a matrix inverse. A matrix is singular iff its determinant is 0.

What is a singular point in calculus?

A singular point of an algebraic curve is a point where the curve has “nasty” behavior such as a cusp or a point of self-intersection (when the underlying field is taken as the reals). More formally, a point on a curve is singular if the and partial derivatives of are both zero at the point . (

What does Bessel mean?

transcendental functions expressible

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What is K in the heat equation?

It is widely used for simple engineering problems assuming there is equilibrium of the temperature fields and heat transport, with time. where u is the temperature, k is the thermal conductivity and q the heat-flux density of the source.

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