We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smooth approximations to solutions of a Hamiltonian system. Our construction of the discrete Lagrangian adopts Hermite interpolation polynomials and the Euler–Maclaurin quadrature formula, and involves applying collocation...

In this study, based on the optimal free derivative without memory methods proposed by Cordero et al. [A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, Mathematical and Computer Modeling. 57 (2013) 1950-1956], we develop two new iterative with memory methods for solving a nonline...

In the present report, Interpolation search, Fast search and Pegasus method are compared with respect to their performance in searching ordered disk files for several key distributions. The aim is to study the effect of the page capacity on searching performance. Cost metric is the number of page accesses and not key comparisons. Numerical results are illustrated and a new approximate formula i...

In an earlier work the author has obtained new quadrature formulas (see (1.3)) based on function values and second derivatives on the zeros of nn(i) as defined by (1.2). The proof given earlier was quite long. The object of this paper is to provide a proof of this quadrature formula which is extremely simple and indeed does not even require the use of fundamental polynomials of (0,2) interpolat...

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

A new rational Krylov method for the efficient solution of nonlinear eigenvalue problems, A(λ)x = 0, is proposed. This iterative method, called fully rational Krylov method for nonlinear eigenvalue problems (abbreviated as NLEIGS), is based on linear rational interpolation and generalizes the Newton rational Krylov method proposed in [R. Van Beeumen, K. Meerbergen, and W. Michiels, SIAM J. Sci....

Clarifying the water invasion rule of edge and bottom reservoirs can adjust reservoir development mode improve recovery factor in a timely manner. Influenced by size body, energy intensity seepage capacity, change model influx basically belongs to exponential growth GM (1,1) or self-constraint logistic model. The above two models are used predict analyze inflow reservoirs, respectively, it is f...

Co-simulation is a widely used solution to enable global simulation of modular system via the composition black-boxed simulators. Among co-simulation methods, IFOSMONDI implicit iterative algorithm, previously introduced by authors, enables us solve non-linear coupling function while keeping smoothness interfaces without introducing delay. Moreover, it automatically adapts size steps between da...

Using dual quaternions, the closure equations of a kinematic loop can be expressed as system multiaffine equations. In this paper, property is leveraged to introduce branch-and-prune method specially tailored for solving such systems The new objectively simpler (in sense that it easier understand and implement) than previous approaches relying on general techniques interval Newton methods or ba...