What is Sturm-Liouville eigenvalue problem?
What is Sturm-Liouville eigenvalue problem?
The problem of finding a complex number µ if any, such that the BVP (6.2)-(6.3) with λ = µ, has a non-trivial solution is called a Sturm-Liouville Eigen Value Problem (SL-EVP). Such a value µ is called an eigenvalue and the corresponding non-trivial solutions y(.; µ) are called eigenfunctions.
What is Sturm-Liouville problem explain?
Sturm-Liouville problem, or eigenvalue problem, in mathematics, a certain class of partial differential equations (PDEs) subject to extra constraints, known as boundary values, on the solutions.
How do you solve the strum Louville problem?
These equations give a regular Sturm-Liouville problem. Identify p,q,r,αj,βj in the example above. y(x)=Acos(√λx)+Bsin(√λx)if λ>0,y(x)=Ax+Bif λ=0. Let us see if λ=0 is an eigenvalue: We must satisfy 0=hB−A and A=0, hence B=0 (as h>0), therefore, 0 is not an eigenvalue (no nonzero solution, so no eigenfunction).
What is Sturm-Liouville boundary value problem?
The so-called Sturm-Liouville Problems define a class of eigenvalue problems, which include many of the previous problems as special cases. The S − L Problem helps to identify those assumptions that are needed to define an eigenvalue problems with the properties that we require.
What is the eigenvalue problem?
The eigenvalue problem (EVP) consists of the minimization of the maximum eigenvalue of an n × n matrix A(P) that depends affinely on a variable, subject to LMI (symmetric) constraint B(P) > 0, i.e.,(11.58)λmax(A(P))→minP=PTB(P)>0.
Which is the Liouvilles formula?
In mathematics, Liouville’s formula, also known as the Abel-Jacobi-Liouville Identity, is an equation that expresses the determinant of a square-matrix solution of a first-order system of homogeneous linear differential equations in terms of the sum of the diagonal coefficients of the system.