We introduce a variation of the proof for weak approximations that is suitable for studying the densities of stochastic processes which are evaluations of the flow generated by a stochastic differential equation on a random variable that may be anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore, if the inve...

in recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. one such method is known as the new extended (g'/g)-expansion method and was proposed by roshid et al. in this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (nlpdes), namely the benjamin-ono equation. it i...

In this paper, optimal control for linear partial differential algebraic equations (PDAE) with quadratic performance is obtained using Simulink. By using the method of lines, the PDAE is transformed into a differential algebraic equations (DAE). Hence, the optimal control of PDAE can be found out by finding the optimal control of the corresponding DAE. The goal is to provide optimal control wit...

This talk deals with the construction of reliable numerical solutions of mixed problems for hyperbolic second order partial differential models with random information in the variable coefficients of the differential equation and in the initial data. Using random difference schemes, a random discrete eigenfunctions method is developed in order to construct a discrete approximating stochastic pr...

Partial fraction expansion is often used with the Laplace Transforms to formulate algebraic expressions for which inverse Transform can be easily found. This paper demonstrates a special case linear, constant coefficient, second order ordinary differential equation no damping term and harmonic function non-homogeneous leads simplified partial due decoupling of coefficients s coefficients. Recog...

Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a SturmLiouville d...