Authors
- R. Farnoosh ^{1}
- H. Rezazadeh ^{} ^{1}
- A. Sobhani ^{1}
- D. Ebrahimibagha ^{2}
^{1} School of Mathematics, Iran University of Science and Technology, 16844, Tehran, Iran
^{2} Department of Mathematics, Center Branch, Islamic Azad university, Tehran, Iran
Abstract
In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differential equations system from this equation, it could be approximated or solved numerically by different numerical methods. In the case of linear stochastic differential equations system by Computing fundamental matrix of this system, it could be calculated based on the exact solution of this system. Finally, this stochastic equation is solved by numerically method like Euler-Maruyama and Milstein. Also its Asymptotic stability and statistical concepts like expectation and variance of solutions are discussed.
Keywords
- Stochastic Differential Equation
- Linear equations system
- Gaussian random variables
- damped harmonic oscillators with noise
- multiplicative noise
Main Subjects