Sturm-Liouville Form Calculator

Sturm-Liouville Form Calculator. The weighting function are given functions; The interested reader can review the literature and more advanced texts for a more in depth.

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Let xbe a fundamental solution of x_ = axwith x(x 0) = x 0. Many classical standard forms can be derived using this substitution. And the eigenvalue is an unspecified parameter.

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First we divide by x to get xy′′ +y′ | {z } (xy′)′ + λ2x − m2 x y = 0. Department of energy's office of scientific and technical information

Then The Sl Di Erential Equation.

The interested reader can review the literature and more advanced texts for a more in depth. Many classical standard forms can be derived using this substitution. Where is a constant and is a known function called either the density or weighting function.

Y00=‚Y:(3) It Follows That If X Is A Solution Of The First Differential Equation In(3)And Y Is A Solution Of The Second Equation In(3),.

Ly(x) = λρ(x)y(x) where ρ(x) 0 is a given real positive weight function and the operator l is. Then detx() = detx 0exp z x x 0 trace(a(s))ds proof. From the robin bc, i get the following trascendental equation for the variable x:

From The Robin Bc, I Get The Following Trascendental Equation For The Variable X:

While the article covers how to get. , , , are given constants; This equation has, for integer ℓ, legendre polnomial solutions pℓ(x).

The Algorithm Works As Follows.

Ly = (p(x)y ′) ′ + q(x)y. V(0) = v0(l) = 0: The weighting function are given functions;

Therefore Is An Eigenvalue Of This Sturm.

So naturally i went looking through my differential calculus textbooks but was surprised they didn't cover this detail. In [2]:= out [2]= plot the eigenfunctions. For example, the associated legendre equation ( 1 − x 2) u ″ − 2 x ( m + 1) u ′ + [ l ( l + 1) − m 2 − m] u = 0 is.