Abstract
The finite set of rate equations C ' m,n =α n,n-1 C m,n-1 (t)+α n,n C m,n (t)+α n,n+1 C m,n+1 (t),
where
are \(\alpha _{j,j - 1} = A,\alpha _{j,j} = - \left( {A + B} \right),\alpha _{j,j + 1} = B\), with \(\alpha _{0,0} = - \alpha _{1,0} = - \alpha\) and \(\alpha _{N,N} = - \alpha _{N - 1,N} = - b,\alpha _{0, - 1} = \alpha _{N,N + 1} = 0\), subject to the initial condition \(C_{m,n} \left( 0 \right) = \delta _{n,m}\) (Kronecker delta) for some \(m\), arises in a number of applications of mathematics and mathematical physics. We show that there are five sets of values of \(a\) and \(b\) for which the above system admits exact transient solutions.
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Parthasarathy, P., Dharmaraja, S. Exact transient solutions of kinetics of first‐order reactions with end effects. Journal of Mathematical Chemistry 25, 281–294 (1999). https://doi.org/10.1023/A:1019153004730
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DOI: https://doi.org/10.1023/A:1019153004730