International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 42389, 29 pages
doi:10.1155/IJMMS/2006/42389
The decomposition method for linear, one-dimensional,
time-dependent partial differential equations
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Received 2 December 2005; Revised 15 May 2006; Accepted 20 June 2006
Copyright © 2006 D. Lesnic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The analytical solutions for linear, one-dimensional,
time-dependent partial differential equations subject
to initial or lateral boundary conditions are reviewed and
obtained in the form of convergent Adomian decomposition power
series with easily computable components. The efficiency and power
of the technique are shown for wide classes of equations of
mathematical physics.