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...

A class of three-pointmethods for solving nonlinear equations of eighth order is constructed. These methods are developed by combining two-point Ostrowski’s fourth-ordermethods and amodified Newton’s method in the third step, obtained by a suitable approximation of the first derivative using the product of three weight functions. The proposed three-step methods have order eight costing only fou...

To solve the heat equation on parallel computers, a high-order finite difference domain decomposition algorithm is discussed. In this procedure, interface values between subdomains are calculated by the classical explicit scheme, while interior values of sub-domains are determined by the famous forth-order compact scheme. The stability and convergence for this domain decomposition algorithm are...

We consider a discretization and the corresponding error analysis for a linear quadratic parabolic optimal control problem with box constraints on the timedependent control variable. For such problems one can show that a time-discrete solution with second order convergence can be obtained by a first order discontinuous Galerkin time discretization for the state variable and either the variation...

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, a new smooth second order sliding mode control is proposed. this algorithm is a modified form of super twisting algorithm. the super twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular lyapunov function. the proposed algorithm which is able to control nonlinear systems with matched structured u...

The variant of Chebyshev-Halley’s method is an iterative used for solving a nonlinear equation with third order convergence. In this paper, we present some new variants three steps free from second derivative two parameters. proposed methods have eighth-order convergence and require four evaluations functions per iteration index efficiency equal to . Numerical simulation will be presented by us...

A theory of third order extended regular variation is developed, somewhat similar to the corresponding theories of first and second order.