Keywords: Volterra integro-differential equations Multistep collocation Superconvergence Stability a b s t r a c t Multistep collocation methods for Volterra integro-differential equations are derived and analyzed. They increase the order of convergence of classical one-step collocation methods, at the same computational cost. The numerical stability analysis is carried out and classes of A 0-s...

Because numerical simulations with classical Johnson-Cook formulation of explosively formed projectiles induce non representative projectiles, a modified Johnson-Cook model taking into account the thermally activated and viscous regimes as well as the notion of saturation stress in the 10 s regime has been developed. Using both models, numerical experimental comparisons of Taylor and explosivel...

Dielectrowetting effects of surface wrinkling, isotropic vs anisotropic spreading, electrode geometry, and deterministic dewetting are presented both experimentally and by 3D numerical modeling. The numerical results are generated by COMSOL in conjunction with the phase-field and electrohydrodynamic methods, including comparisons to experimental data. The dynamic behavior of the two-phase syste...

Abstract: In this study, we present a numerical scheme to solve the telegraph equation by using Fibonacci polynomials. This method is based on the Fibonacci collocation method which transforms the equation into a matrix equation, and the unknown of this equation is a Fibonacci coefficients matrix. Some numerical examples with comparisons are included to demonstrate the validity and applicabilit...

We present a modified version of the approximate minimum degree algorithm for preordering a matrix with a symmetric sparsity pattern prior to the numerical factorization. The modification is designed to improve the efficiency of the algorithm when some of the rows and columns have significantly more entries than the average for the matrix. Numerical results are presented for problems arising fr...

Parallel computation fortwo-dimensionat co)wective flows in cavities with adiabatic horizontal boundaries and driven by differential heating of the two vertical end walk, are investigated using the Intel Paragon, Intel Touchstone Delta, and Cray 13D. I’he numerical scheme, including a parallel multigrid solver, and domain decomposition techniques for parallel computing are discussed in detail. ...

A class of ^-stable advanced multistep methods is derived for the numerical solution of initial value problems in ordinary differential equations. The methods, of all orders of accuracy up to ten, only require values of y' and are self starting. Results for the asymptotic behaviour of the discretization error and for estimating local truncation error are also obtained. The practical implementat...

The recently developed multiscale kernel of R. Opfer is applied to approximate numerical derivatives. The proposed method is truly mesh-free and can handle unstructured data with noise in any dimension. The method of Tikhonov and the method of L-curve are employed for regularization; no information about the noise level is required. An error analysis is provided in a general setting for all dim...

Efficient numerical techniques for multivariable system identification and model reduction are investigated. The techniques are implemented in the system identification and model reduction toolboxes based on the Fortran 77 Subroutine Library in Control Theory (SLICOT). Besides highly performant Fortran drivers and computational routines, these toolboxes provide MATLAB or Scilab interfaces, impl...

After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations in one horizontal dimension. The numerical discretization is validated by comparisons with analytical, experimental data or other numerical solutions obtained...