the aim of the present paper is the investigation of some problems which can be reduced to thegoursat problem for a third order equation. some results and theorems are given concerning the existence anduniqunce for solving the suggested problem.

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...

The framework of first-, second-, and third-order embodiment (1-3E; Metzinger, 2014) was developed for exploring how phenomenal properties are physically and computationally grounded. Metzinger’s goal for 1-3E is to show how the experience of being a self (i.e., phenomenal selfhood) is generated within an embodied system and thus to embed his self-model theory (Metzinger, 2004) in the context o...

In this paper, it is tried to find an approximate single layer equivalent for multi-layer graphene sheets based on third order non-local elasticity theory. The plates are embedded in two parameter Winkler-Pasternak elastic foundation, and also the thermal effects are considered. A uniform transverse load is imposed on the plates. Applying the non-local theory of Eringen based on third order she...

We analytically calculate the perturbation expansion of two-point correlation function (propagator) scalar, dissipative quantum ${\ensuremath{\varphi}}^{4}$ theory up to third order in interaction parameter $\ensuremath{\lambda}$. The calculations are carried out with two different methods. first is based on a brute force computation all interactions appearing term by at given perturbation, sup...