first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

This paper introduces higher-order solutions of the quadratic nonlinear stochastic oscillatory equation. Solutions with different orders and different number of corrections are obtained with the WHEP technique which uses the WienerHermite expansion and perturbation technique. The equivalent deterministic equations are derived for each order and correction. The solution ensemble average and vari...

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dB (H) (t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solut...

Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...

We consider stochastic semilinear partial differential equations with Lipschitz nonlinear terms. We prove existence and uniqueness of an invariant measure and the existence of a solution for the corresponding Kolmogorov equation in the space L(H ; ν), where ν is the invariant measure. We also prove the closability of the derivative operator and an integration by parts formula. Finally, under bo...

We have significant accomplishments on uncertainty quantification in inverse problems for dynamical systems, generalized sensitivity and optimal design of experiments, elasticity and viscoelasticity modeling for buried target detection, and general inverse problem methodology for proliferating populations. Our efforts have continued on development of efficient accurate integration of Fokker Pla...

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

Self-stabilizing diffusions are stochastic processes, solutions of nonlinear stochastic differential equation, which are attracted by their own law. This specific self-interaction leads to singular phenomenons like non uniqueness of associated stationary measures when the diffusion leaves in some non convex environment (see [5]). The aim of this paper is to describe these invariant measures and...

In this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy Fredholmintegro-differential equation of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an it...

This thesis is devoted to the study of stochastic nonlinear Schrödinger equations (abbreviated as SNLS) with linear multiplicative noise in two aspects: the wellposedness in L(R), H(R) and the noise effects on blowup phenomena in the non-conservative case. 1. The well-posedness in L(R). The first fundamental question when dealing with SNLS is the well-posedness problem. In the first chapter, we...