Achieving improved order of accuracy for a hydrodynamic numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. This paper presents a weak statement perturbation methodology retaining block-tridiagonal forms that can reduce, or annihilate in special cases, the Taylor series truncation error to hi...

A new Taylor series method that the authors originally developed for the solution of one-dimensional integral equations is extended to solve multivariate integral equations. In this paper, the new method is applied to the solution of multivariate Fredholm equations of the second kind. A comparison is given of the new method and the traditional Taylor series method of solving integral equations....

An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equilibrium, the Taylor series involving multilinear forms which are uniquely characterized by generalized Lyapunov equations. A numerical method for solving these equations is proposed. It is based on a generalization of ...

Using numerical simulations of lattice QCD we calculate the effect of an external magnetic field on the equation of state of the quark-gluon plasma. The results are obtained using a Taylor expansion of the pressure with respect to the magnetic field for the first time. The coefficients of the expansion are computed to second order in the magnetic field. Our setup for the external magnetic field...

We consider second order linear differential equations in a real interval I with mixed Dirichlet and Neumann boundary data. We consider a representation of its solution by a multi-point Taylor expansion. The number and location of the base points of that expansion are conveniently chosen to guarantee that the expansion is uniformly convergent ∀ x ∈ I. We propose several algorithms to approximat...

In this talk we extend the Polyakov-quark-meson model to N f = 2 + 1 quark flavors and study its bulk thermodynamics at finite temperatures in mean-field approximation. Three different Polyakov-loop potentials are considered. Our findings are confronted to recent QCD lattice simulations of the RBC-Bielefeld and HotQCD collaborations. Furthermore, the finite chemical potential expansion of the q...

Properties of QCD at finite chemical potential (μ) are extracted using Taylor series expansions. The continuum limits of lattice results are presented. The result of expanding the free energy density, i. e., the pressure, to 6th order in the expansion is shown. The Taylor coefficients of the chiral condensate are also shown. Relations between various Taylor coefficients are demonstrated. All th...

in this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the hunter-saxton equation. the main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. it is a semi analytical-numerical metho...