A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

In the past two decades, due to study on matrix theory and some engineering background problems, many scholars dedicated to special matrix , and obtained some important and valuable results (TingZhu, 2007 Yigeng Huang, 1994). But in combination matrix theory, combinatorics, probability theory (especially Markov chain), mathematical economics and reliability theory etc. areas there is a special ...

Stochastic parametrization provides a methodology for representing model uncertainty in ensemble forecasts, and also has the capability of reducing systematic error through the concept of nonlinear noise-induced rectification. The stochastically perturbed parametrization tendencies scheme and the stochastic backscatter scheme are described and their impact on medium-range forecast skill is disc...

In this paper, operational matrix method based upon the Bernstein polynomials is proposed to solve the variable order fractional integro-differential equations in the Caputo derivative sense. We derive the Bernstein polynomials operational matrix of fractional order integration and introduce the product operational matrix of Bernstein polynomials. A truncated the Bernstein polynomials series to...

In this paper, we propose a new ridge-type estimator called the new mixed ridge estimator (NMRE) by unifying the sample and prior information in linear measurement error model with additional stochastic linear restrictions. The new estimator is a generalization of the mixed estimator (ME) and ridge estimator (RE). The performances of this new estimator and mixed ridge estimator (MRE) against th...

in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...