Research ArticleOpen AccessGoogle Scholar indexed
A Note on Differential Equation with a Large Parameter
Department of Mathematics Michael Okpara, University of Agriculture, Umudike, Nigeria
Department of Mathematics Michael Okpara, University of Agriculture, Umudike, Nigeria
- 1 Department of Mathematics Michael Okpara, University of Agriculture, Umudike, Nigeria
- 2 Department of Mathematics Michael Okpara, University of Agriculture, Umudike, Nigeria
Applied Mathematics·Volume 07 (2016)·Pages 183–192·Published 24 February 2016·DOI10.4236/am.2016.73018
Copy link · social · email
Abstract
We present here asymptotic solutions of equations of the type , where is a large parameter. The Bessel differential equation is considered as a typical example of the above and the solutions are provided as . Furthermore, the behaviour of the solutions as well as the stability of the Bessel ode is investigated numerically as the parameter grows indefinitely.
KeywordsODEAsymptotic SolutionsBessel Differential EquationStabilityMathCAD Solution
- Olver, F.W.J. (1997) Asymptotics and Special Functions. Academic Press, New York. Reprinted by AK Peters, Wellesley.
- Shkil, M.I. (1971) Asymptotic Methods in Differential Equations. Vyshcha Shkola, Kyiv, 228 p.
- Territin, Kh.L. (1957) Asymptotic Expansion of Solutions to System of Ordinary Differential Equations Containing Parameter. Matematika: Sb. per., 1, 29-59.
- Tikhonov, A. (1948) On Dependence of Solutions of Differential Equations on Small Parameter. Mat. Sb., 28, 193-204.
- MathSoft, Inc. (1997) MathCAD 7 User’s Guide. http://www.mathsoft.com