An A-stable Explicit Numerical Integration Method Based on Padé Approximation

On Padé Approximation of Some Practical Functions

Computation of Numerical Padé-Hermite and Simultaneous Padé Systems II: A Weakly Stable Algorithm

For k + 1 power series a0(z), . . . , ak(z), we present a new iterative, look-ahead algorithm for numerically computing Padé-Hermite systems and simultaneous Padé systems along a diagonal of the associated Padé tables. The algorithm computes the systems at all those points along the diagonal at which the associated striped Sylvester and mosaic Sylvester matrices are wellconditioned. The operati...

An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity

This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are p...

Approximation, Numerical Differentiation and Integration Based on Taylor Polynomial

We represent new estimates of errors of quadrature formula, formula of numerical differentiation and approximation using Taylor polynomial. To measure the errors we apply representation of the remainder in Taylor formula by least concave majorant of the modulus of continuity of the n−th derivative of an n−times differentiable function. Our quantitative estimates are special applications of a mo...

An Interpolation Approximation for the GI/G/1 Queue Based on Multipoint Padé Approximation

The performance evaluation of many complex manufacturing, communication and computer systems has been made possible by modeling them as queueing systems. Many approximations used in queueing theory have been drawn from the behavior of queues in light and heavy tra c conditions. In this paper, we propose a new approximation technique, which combines the light and heavy tra c characteristics. Thi...