Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran
Abstract
In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation which can be solved by some numerical methods like Newton's or Broyden's methods. The capability of the simulation of Brownian motion with Schauder functions which are the integration of Haar functions enables us to find some reasonable approximate solutions. Two test examples and the application of the presented method for the general stock model are considered to demonstrate the efficiency, high accuracy and the simplicity of the presented method.
Vahdati, S. (2017). A wavelet method for stochastic Volterra integral equations and its application to general stock model. Computational Methods for Differential Equations, 5(2), 170-188.
MLA
Vahdati, S. . "A wavelet method for stochastic Volterra integral equations and its application to general stock model", Computational Methods for Differential Equations, 5, 2, 2017, 170-188.
HARVARD
Vahdati, S. (2017). 'A wavelet method for stochastic Volterra integral equations and its application to general stock model', Computational Methods for Differential Equations, 5(2), pp. 170-188.
CHICAGO
S. Vahdati, "A wavelet method for stochastic Volterra integral equations and its application to general stock model," Computational Methods for Differential Equations, 5 2 (2017): 170-188,
VANCOUVER
Vahdati, S. A wavelet method for stochastic Volterra integral equations and its application to general stock model. Computational Methods for Differential Equations, 2017; 5(2): 170-188.
)
