In this article, a new numerical method based on triangular functions for solving  nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and eff...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

for the nonlinear analysis of structures using the well known newton-raphson method, the tangent stiffness matrices of the elements must be constructed in each iteration. due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the newton-raphson method to reduce the cost and time required by the analysis. in this paper, a ...

Abstract: In this work, the operational Tau method is presented to find the solutions of the linear and nonlinear Volterra-Fredholm-Hammerstein integral equations (VFHIEs) of the second kind. Some simple matrices in extension of Tau method for the numerical solutions of VFHIEs is applied. In fact, operational Tau method converts the integral parts of the desired VFHIEs to some operational matri...

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

By the method of integral and hybrid transforms in combination with principal solutions (matrices influence Green’s matrices), we construct, for first time, unique exact analytic parabolic boundary-value problems mathematical physics a piecewise homogeneous wedge-shaped cylindrically circular space.

Recent work in compressed sensing theory shows that n×N independent and identically distributed (IID) sensing matrices whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal with high probability even if n N . Motivated by signal processing applications, random filtering with Toeplitz sensing matrices whose elements are drawn fro...

We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the limiting distribution of large random matrices, we also found that the Tracy-Widom law can be approximated by a properly scaled and shifted gamma distribution, with...

In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...