Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics.

Finite-Difference and Pseudo-Sprectral Methods for the Numerical Simulations of In Vitro Human Tumor Cell Population Kinetics

Numerical resolution of large deflections in cantilever beams by Bernstein spectral method and a convolution quadrature.

The mathematical modeling of the large deflections for the cantilever beams leads to a nonlinear differential equation with the mixed boundary conditions. Different numerical methods have been implemented by various authors for such problems. In this paper, two novel numerical techniques are investigated for the numerical simulation of the problem. The first is based on a spectral method utiliz...

Scalable Arbitrary-Order Pseudo-Spectral Electromagnetic Solver

Numerical simulations have been critical in the recent rapid developments of advanced accelerator concepts. Among the various available numerical techniques, the ParticleIn-Cell (PIC) approach is the method of choice for self-consistent simulations from first principles, and although the fundamentals of the PIC method were established decades ago, improvements or variations still continue to ar...

Detailed comparison of numerical methods for the perturbed sine-Gordon equation with impulsive forcing

The properties of various numerical methods for the study of the perturbed sine-Gordon (sG) equation with impulsive forcing are investigated. In particular, finite difference and pseudo-spectral methods for discretizing the equation are considered. Different methods of discretizing the Dirac delta are discussed. Various combinations of these methods are then used to model the soliton–defect int...

Vibration and Stability of Axially Moving Plates by Standard and Spectral Finite Element Methods

Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...