ISSN:
1573-8795
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider the finite-difference eigenvalue problem u xx − + λu=0, u0= un+1=0 on a nonuniform grid ω=xi∶i=0,1,...,n+1, x0=0, xn+1=1. In connection with the issue of existence of exact-spectrum schemes for second-derivative operators, we examine the extremal properties of functions fn(v, h)=λ1 v(h)+ ...+λn v(h), v ∈ R. We prove that the maximum of fn(−1, h) is attained only on a uniform grid. We establish a necessary condition for given numbers 0 〈λ1 〈... 〈 λn to be the eigenvalues of the above problem for at least one grid ω.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01142520
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