Explicit numerical methods for the solution of a system of stiff differential equations suffer from a time step size that approaches zero in order to satisfy stability conditions. Implicit schemes allow a larger time-step, but require more computations. When the differential equations are dominated by a skew-symmetric component, the problem is not stiffness in the sense that the size of the eig...

We discuss the implications of the recently reported RK and RK∗ anomalies, the lepton flavor non-universality in the B → Kll and B → Kll. Using two sets of hadronic inputs of form factors, we perform a fit of the new physics to the RK and RK∗ data, and significant new physics contributions are found. We propose to study the lepton flavor universality in a number of related rare B,Bs, Bc and Λb ...

We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a ‘small’ deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of discontinuous groups, we introduce the concepts from a group theoretic perspectiv...

We study the spatial semidiscretizations obtained by applying Runge–Kutta (RK) and partitioned Runge–Kutta (PRK) methods to multisymplectic Hamiltonian partial differential equations. These methods can be regarded as multisymplectic hp-finite element methods for wave equations. All the methods we consider are multisymplectic; we determine their properties with regard to existence of solutions, ...

We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a ‘small’ deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of discontinuous groups, we introduce the concepts from a group theoretic perspectiv...

Abstract Three prominent low order implicit time integration schemes are the first Euler-method, second trapezoidal rule and Ellsiepen method. Its advantages stability comparatively computational cost, however, they require solution of a nonlinear system equations. This paper presents general approach for construction third Runge–Kutta methods by embedding above mentioned into class ELDIRK-meth...

The Kohn-Sham equation in first-principles density functional theory (DFT) calculations is a nonlinear eigenvalue problem. Solving the nonlinear eigenproblem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshevfiltered subspace iteration (CheFSI) ...

Salinity is an important factor in reduced cucumber yield and quality. Grafting on the resistant rootstock could keep growth near to optimum condition. The aim of the present research is to investigate the characteristics of different rootstocks on physiology and fruit characteristics of cucumber. Treatments were rootstocks [Rn: Nongrafted (Cucumis sativus v. DAVOSII), Rt: Tanbal (Cucurbita max...

The fractional step method is a technique that results in a computationally-efficient implementation of Navier–Stokes solvers. In the finite element-based models, it is often applied in conjunction with implicit time integration schemes. On the other hand, in the framework of finite difference and finite volume methods, the fractional step method had been successfully applied to obtain predicto...

In order to solve general seventh-order ordinary differential equations (ODEs), this study will develop an implicit block method with three points of the form y(7)(ξ)=f(ξ,y(ξ),y′(ξ),y″(ξ),y‴(ξ),y(4)(ξ),y(5)(ξ),y(6)(ξ)) directly. The Hermite interpolation in (GIBM3P) has been derived initial value problems (IVPs) using basic functions interpolating polynomials. A multi-step is constructed be sui...