ANZIAM J. 47(EMAC2005) pp.C245--C260, 2006.
On approximate closed form solutions of linear ordinary differential equations
F. Viera |
Abstract
Approximate closed form solutions of a linear ordinary differential equation are obtained using piecewise approximations of the arbitrary coefficient function. We show how to obtain expressions for the general solution and the eigenvalue equation. An example is given with specific boundary conditions typical of a range of problems in mathematical physics and engineering. The method is robust and accurate and can be used as a complement to standard numerical techniques. The function representing the approximate solution has a simple form and can be used like a standard function in calculations that require the solution of the differential equation.
Download to your computer
- Click here for the PDF article (235 kbytes) We suggest printing 2up to save paper; that is, print two e-pages per sheet of paper.
- Click here for its BiBTeX record
Authors
- F. Viera
- School of Science & Technology, Charles Sturt University, Wagga Wagga, Australia. mailto:fviera@csu.edu.au
Published September 18, 2006. ISSN 1446-8735
References
- Rayleigh Lord (Strutt J. W.), 1912, Proc. Roy. Soc. A, 86, 207. http://www.journals.royalsoc.ac.uk/link.asp?id=eg142ju756873wl3
- Y. B. Chernyak, On a fitting technique approach in potential scattering theory, J. Phys. A: Math. Gen., Vol. 10, No 9, 1477, 1977. http://dx.doi.org/10.1088/0305-4470/10/9/009
- T. M. Kalotas and A. R. Lee, A new approach to one-dimensional scattering, Am. J. Phys., Vol. 59, 48--52, 1991. http://dx.doi.org/10.1119/1.16705
- L. D. Landau, E. M. Lifshitz, Quantum Mechanics. Non-Relativistic theory. 3rd Edn. London: Pergamon. 1977.
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.