A matrix method for ordinary differential eigenvalue problems
Abstract
This paper describes a method for solving ordinary differential eigenvalue problems of the form N( u) + λM( u) = 0, where N and M are linear differential operators and u(x) is a scaler variable. The boundary conditions are independent of λ. The problem is transformed into a matrix problem ∥ A + λB ∥ = 0. This is reduced to the standard eigenvalue problem ∥ Â + λI ∥ = 0 which is then solved by the Q  R algorithm. The computer program is organized so that it can solve a wide range of problems with minimal effort on the user's part. The method is applied to a hydrodynamic stability problem and compared to the shooting method.
 Publication:

Journal of Computational Physics
 Pub Date:
 April 1970
 DOI:
 10.1016/00219991(70)900586
 Bibcode:
 1970JCoPh...5..169G