An efficient computational method for solving nonlinear stochastic It(o)over-cap integral equations: Application for stochastic problems in physics

作者：Heydari M H^*; Hooshmandasl M R; Cattani C; Ghaini F M Maalek

来源：Journal of Computational Physics, 2015, 283: 148-168.

DOI：10.1016/j.jcp.2014.11.042

• Generalized hat basis functions
• Stochastic operational matrix
• Nonlinear stochastic It(o)over-cap integral equations
• It(o)over-cap integral
• Brownian motion process
• Stochastic population growth models
• Stochastic pendulum problems

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of It (o) over cap -integration is proposed for solving nonlinear stochastic Ito integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.

• 出版日期2015-2-15