Rezazadeh, H., Maghasedi, M., shojaee, B. (2012). Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation. Journal of Linear and Topological Algebra (JLTA), 01(02), 83-95.

H. R. Rezazadeh; M. Maghasedi; B. shojaee. "Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation". Journal of Linear and Topological Algebra (JLTA), 01, 02, 2012, 83-95.

Rezazadeh, H., Maghasedi, M., shojaee, B. (2012). 'Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation', Journal of Linear and Topological Algebra (JLTA), 01(02), pp. 83-95.

Rezazadeh, H., Maghasedi, M., shojaee, B. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation. Journal of Linear and Topological Algebra (JLTA), 2012; 01(02): 83-95.

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

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

Abstract

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.