Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Subject Areas : History and biography

H. R. Rezazadeh ¹ (Department of Mathematics, Karaj Branch, Islamic Azad University, PO. Code 31485-313, Karaj, Iran)
M. Maghasedi ² (Department of Mathematics, Karaj Branch, Islamic Azad University, PO. Code 31485-313, Karaj, Iran)
B. shojaee ³ (Department of Mathematics, Karaj Branch, Islamic Azad University, PO. Code 31485-313, Karaj, Iran)

Received: 2012-01-01 Accepted : 2012-01-01 Published : 2012-06-01

Keywords: Linear equations system, Heun equation, Wiener process, Stochastic Differential Equation,

Abstract :

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

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