IJPAM: Volume 93, No. 6 (2014)

GENERAL SOLUTION TO BATEMAN'S DIFFERENTIAL
EQUATIONS WITH DIRECT INDEX NOTATION

Ronaldo Thibes$^1$, Suzicleide L. de Oliveira$^2$
$^{1,2}$Departamento de Ciências Exatas e Naturais
Universidade Estadual do Sudoeste da Bahia
Itapetinga - BA, BRAZIL


Abstract. Bateman's equations describe a system of radioactive decay of different products in chain. We provide an explicit proof of the general solution to Bateman's equations by direct attack. By using index notation of ordinary sums and products the system of $k$ differential equations can be shown to be easily solved. We compare our method with previous more elaborated ones published in the literature.

Received: April 23, 2014

AMS Subject Classification: 34A05, 81V35

Key Words and Phrases: differential equations, ode, nuclear decay, index notation

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DOI: 10.12732/ijpam.v93i6.11 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 6
Pages: 879 - 883

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).