in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

We study backward stochastic Riccati equations (BSREs) arising in quadratic optimal control problems with infinite dimensional stochastic differential state equations. We allow the coefficients, both in the state equation and in the cost, to be random. In such a context BSREs are backward stochastic differential equations living in a non-Hilbert space and involving quadratic non-linearities. We...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

This paper is an extension of previous work where we laid the foundation for the kernel-based collocation solution of stochastic partial differential equations (SPDEs), but dealt only with the simpler problem of right-hand-side Gaussian noises. In the present paper we show that kernel-based collocation methods can be used to approximate the solutions of high-dimensional elliptic partial differe...

in previous studies we first concentrated on utilizing crisp simulationto produce discrete event fuzzy systems simulations. then we extendedthis research to the simulation of continuous fuzzy systems models. in this paperwe continue our study of continuous fuzzy systems using crisp continuoussimulation. consider a crisp continuous system whose evolution depends ondifferential equations. such a ...

This thesis investigates the possibility of approximating stationary solutions of stochastic differential equations using numerical methods. We consider a particular class of stochastic differential equations, which are known to generate random dynamical systems. The existence of stochastic stationary solution is proved using global attractor approach. Euler’s numerical method, applied to the s...

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

An available method of modeling and predicting the economic time series is the use of stochastic differential equations, which are often determined as jump-diffusion stochastic differential equations in financial markets and underlier economic dynamics. Besides the diffusion term that is a geometric Brownian model with Wiener random process, these equations contain a jump term that follows Pois...

For nonlinear random operator equations where the distributions of the stochastic inputs are approximated by sequences of random variables converging in distribution and where the underlying deterministic equations are simultaneously approximated, we prove a result about tightness and convergence in distribution of the approximate solutions. We apply our result to a random differential equation...

In this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains. By employing shape sensitivity analysis, we linearize the influence of the random domain perturbation on the solution. We derive deterministic partial differential equations to approximate the random solution’s mean and its covariance wit...