Eigenvalue Problems

  • Granville Sewell


The form of the eigenvalue PDE system solved by PDE/PROTRAN (Section 1.5) is:
$$\begin{array}{*{20}{c}} {0 = {A_x}(x,y,u,{u_x},{u_y}) + {B_y}(x,y,u,{u_x},{u_y}) + F(x,y,u,{u_x},{u_y}) + \lambda P(x,y)u\,in\,R} \\ {u = 0\,on\,\partial {R_1}} \\ {A{n_x} + B{n_y} = GB(x,y,u)\,on\,\partial {R_2}} \end{array}$$
where A, B, F and GB are linear, homogeneous functions and P is a (usually diagonal) matrix.


Stationary Point Small Eigenvalue Discrete Problem Inverse Power Essential Boundary Condition 
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  1. 1.
    Varga, R.S., Functional Analysis and Approximation Theory in Numerical Analysis, Regional Conference Series in Applied Mathematics, SIAM, 1971.MATHCrossRefGoogle Scholar
  2. 2.
    Fox, L., Henrici, P., Moler, C., “Approximations and Bounds for Eigenvalues of Elliptic Operators,” Si am J. Numer. Anal. 4 (1967) pp 89–102.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

  • Granville Sewell
    • 1
  1. 1.Mathematics DepartmentUniversity of Texas at El PasoEl PasoUSA

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