Mimetic Methods on Measure Chains
We introduce the divergence and the gradient for functions defined on a measure chain, and this includes as special cases both continuous derivatives and discrete forward differences. It is shown that in one dimension, subject to Dirichlet boundary conditions, the divergence and the gradient are negative adjoints of each other and that the divergence of the gradient is negative semidefinite. These are well-known results in the continuous their, and hence, mimic those properties also for the case of a general measure chain.
M. Bohner and J. E. Castillo, "Mimetic Methods on Measure Chains," Computers & Mathematics with Applications, Elsevier, Jan 2001.
The definitive version is available at http://dx.doi.org/10.1016/S0898-1221(01)00189-4
Mathematics and Statistics
Keywords and Phrases
time scales; measure chains; mimetic properties; divergence; Gradient; Laplacian
Article - Journal
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