In this paper, an extension of DIFFERENTIAL Transformation Method (DTM) which is an analytical-numerical method for solving the fuzzy PARTIAL DIFFERENTIAL EQUATION (FPDE) by using the strongly generalized differentiability concept is investigated. The proposed algorithm is illustrated by numerical example.

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. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding DIFFERENTIAL EQUATIONs.

The aim of this manuscript is to introduce and analyze a STOCHASTIC finite difference  scheme for Ito STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONs. We also discuss the consistency, stability, and convergence for the STOCHASTIC finite difference scheme. The numerical simulations obtained from the proposed  STOCHASTIC finite difference scheme show the efficiency of the suggested  STOCHASTIC finite difference scheme.

The main issue in any image zooming techniques is to preserve the structure of the zoomed image. The zoomed image may suffer from the discontinuities in the soft regions and edges; it may contain artifacts, such as image blurring and blocky, and staircase effects. This paper presents a novel image zooming technique using PARTIAL DIFFERENTIAL EQUATIONs (PDEs). It combines a non-linear Fourth-order PDE method with the Locally Adaptive Zooming (LAZ) algorithm. The proposed method uses high-resolution image obtained from LAZ algorithm to construct zoomed image by Fourth-order PDE. This proposed method preserves edges and minimizes blurring and staircase effects in the zoomed image. In order to evaluate image quality obtained from the proposed method, this paper focuses on both subjective and objective assessments. The results of these measures on a variety of images show that the proposed method is superior over the other image zooming methods.

The purpose of this article is modeling the behavior of stock price using STOCHASTIC DIFFERENTIAL EQUATIONs. The data for this study include daily observations of the total stock market index, the index of the top 50 companies and the index of the 30 largest companies in the Tehran Stock Exchange. The data are daily from March 25, 2006 to April 15, 2015.The geometric Brownian motion and geometric Brownian motion with nonlinear GARCH are used to modeling the behavior of price index. The results of this study includes the following: (1) According to the log likelihood function, geometric Brownian motion with nonlinear GARCH in the three groups studied data has better performance than the geometric Brownian motion. (2) Based on the model of STOCHASTIC DIFFERENTIAL EQUATIONs with STOCHASTIC volatility, the total market index is more influenced by the good news. (3) The impact of the bad news on the index of the 30 largest companies is more than the impact of the good news. (4) The unconditional variance of the total stock market index has two structural breaks; the unconditional variance of index of the top 50 companies has one structural break and no structural breaks in the unconditional variance of index of the 30 largest companies.