A computational method for solving stochastic Ito-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions

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

来源：Journal of Computational Physics, 2014, 270: 402-415.

DOI：10.1016/j.jcp.2014.03.064

• Generalized hat basis functions
• Stochastic operational matrix
• Stochastic Ito Volterra integral equations
• Ito integral
• Brownian motion process

In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Ito-Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0, T] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by forward substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O(1/n(2)). Further, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method.

• 出版日期2014-8-1