Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Journal of Linear and Topological Algebra

مقاله 4، دوره 01، شماره 02، شهریور 2012، صفحه 83-95   

نویسندگان

H. R. Rezazadeh^* ؛ M. Maghasedi؛ B. shojaee

Department of Mathematics, Karaj Branch, Islamic Azad University, PO. Code 31485-313, Karaj, Iran

چکیده

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

کلیدواژه‌ها

Heun equation؛ Wiener process؛ Stochastic Differential Equation؛ Linear equations system

مراجع

[1] L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, (1974).

[2] D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differ- ential equations, SIAM Review 43 (2001), 525–546.

[3] J. Lamperti, A simple construction of certain diffusion processes, J. Math. Kyoto (1964), 161–170.

[4] H. McKean, Stochastic Integrals, Academic Press, (1969).

[5] B. K. Oksendal, Stochastic Differential Equation with Applications, 4th ed., Springer (1995).

[10] S. Slavyanov, W. Lay.: Special Functions, A Unified Theory Based on Singularities, Oxford Univ. Press, Oxford.(2000).

[11] R.S. Borissov, P.P. Fiziev.: Exact Solutions of Teukolsky Master Equation with Continuous Spectrum. Bulg. J. Phys. 37 (2010) 65–89.

[12] P.P. Fiziev, Journal of Physics-Mathematical and Theoretical 43, 035203(2010).

[13] Slavyanov, S.Y., and Lay, W. Special Functions, A Unified Theory Based on Singularities. Oxford Mathematical Monographs, (2000).

[14] Ronveaux, A. ed. heun’s Differential Equations. Oxford University Press, (1995).