1

December 2017
Applied Mathematics and Computation: Volume 314 Issue C, December 2017

**Publisher:** Elsevier Science Inc.

In this paper, we consider a regular grid with equal spatial spacings and construct a new finite difference approximation (difference scheme) for the system of two-dimensional NavierStokes equations describing the unsteady motion of an incompressible viscous liquid of constant viscosity. In so doing, we use earlier constructed discretization of the ...

**Keywords**:
2D NavierStokes equations, Primary 12H10, Secondary 13P10, Finite difference method, Strong consistency, Difference algebra, Grbner bases

2

August 2015
Advances in Computational Mathematics: Volume 41 Issue 4, August 2015

**Publisher:** Springer-Verlag New York, Inc.

We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with the analytical solution. We apply the methods to locate periodic orbits in ...

**Keywords**:
Optimal control, 65L10, 65P10, 65L06, Astrodynamics, Energy conserving Runge---Kutta methods, Hamiltonian boundary value problems

3

September 2013
CASC 2013: Proceedings of the 15th International Workshop on Computer Algebra in Scientific Computing - Volume 8136

**Publisher:** Springer-Verlag New York, Inc.

In the given paper, we confront three finite difference approximations to the Navier—Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these approximations were generated by the computer algebra assisted method proposed based on the finite volume method, numerical integration, and difference elimination. The third approximation was derived ...

4

October 2012
Journal of Computational and Applied Mathematics: Volume 236 Issue 16, October, 2012

**Publisher:** Elsevier Science Publishers B. V.

We show the main features of the MATLAB code HOFiD_UP for solving second order singular perturbation problems. The code is based on high order finite differences, in particular on the generalized upwind method. Within its simplicity, it uses order variation and continuation for solving any difficult nonlinear scalar problem. Several ...

**Keywords**:
Two-point boundary value problems, Codes for BVPs, Finite difference schemes, Singular perturbation problems

5

March 2009
Applied Numerical Mathematics: Volume 59 Issue 3-4, March, 2009

**Publisher:** Elsevier Science Publishers B. V.

The parallel solution of initial value problems for ordinary differential equations (ODE-IVPs) has received much interest from many researchers in the past years. In general, the possibility of using parallel computing in this setting concerns different aspects of the numerical solution of ODEs, depending on the parallel platform to be ...

**Keywords**:
“Parareal” algorithm, 65L06, Boundary Value Methods (BVMs), Ordinary Differential Equations, Parallel factorizations, Parallel methods “in time” for ODEs, Stiff Problems, 65H10, 65L05, Initial Value Problems, Parallel Computing, 65L80, Block one step methods

6

December 2006
ACM Transactions on Mathematical Software (TOMS): Volume 32 Issue 4, December 2006

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 2

Downloads (6 Weeks): 3, Downloads (12 Months): 15, Downloads (Overall): 365

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BABDCR is a package of Fortran 90 subroutines for the solution of linear systems with bordered almost block diagonal coefficient matrices. It is designed to handle matrices with blocks of the same size, that is, having a block upper bidiagonal structure with an additional block in the right upper corner. ...

**Keywords**:
Linear systems, bordered almost block diagonal matrices, numerical solution, cyclic reduction

7

March 2006
Future Generation Computer Systems: Volume 22 Issue 4, March 2006

**Publisher:** Elsevier Science Publishers B. V.

Given a Hamiltonian matrix H = JS with S symmetric and positive definite, we analyze a symplectic Lanczos algorithm to transform - H 2 in a symmetric and positive definite tridiagonal matrix of half size. By means of two effective restarted procedures, this algorithm is then used to compute few ...

**Keywords**:
Lanczos algorithm, Hamiltonian matrices, eigenvalues

8

March 2006
Future Generation Computer Systems: Volume 22 Issue 4, March 2006

**Publisher:** Elsevier Science Publishers B. V.

Given a Hamiltonian matrix H=JS with S symmetric and positive definite, we analyze a symplectic Lanczos algorithm to transform -H^2 in a symmetric and positive definite tridiagonal matrix of half size. By means of two effective restarted procedures, this algorithm is then used to compute few extreme eigenvalues of H. ...

**Keywords**:
Hamiltonian matrices, Eigenvalues, Lanczos algorithm

9

April 2005
Journal of Computational and Applied Mathematics: Volume 176 Issue 1, 1 April 2005

**Publisher:** Elsevier Science Publishers B. V.

We introduce new methods in the class of boundary value methods (BVMs) to solve boundary value problems (BVPs) for a second-order ODE. These formulae correspond to the high-order generalizations of classical finite difference schemes for the first and second derivatives. In this research, we carry out the analysis of the ...

**Keywords**:
conditioning analysis, finite difference schemes, boundary value methods, two-point boundary value problems

10

April 2005
Journal of Computational and Applied Mathematics: Volume 176 Issue 1, 1 April 2005

**Publisher:** Elsevier Science Publishers B. V.

We introduce new methods in the class of boundary value methods (BVMs) to solve boundary value problems (BVPs) for a second-order ODE. These formulae correspond to the high-order generalizations of classical finite difference schemes for the first and second derivatives. In this research, we carry out the analysis of the ...

**Keywords**:
65L10, 65L12, Boundary value methods, Conditioning analysis, Finite difference schemes, 65L20, Two-point boundary value problems

11

December 2004
CIS'04: Proceedings of the First international conference on Computational and Information Science

**Publisher:** Springer-Verlag

We solve nonlinear elliptic PDEs by stable finite difference schemes of high order on a uniform meshgrid. These schemes have been introduced in [1] in the class of Boundary Value Methods (BVMs) to solve two-point Boundary Value Problems (BVPs) for second order ODEs and are high order generalizations of classical ...

**Keywords**:
elliptic PDEs, finite differences, boundary value methods

12

June 2003
ICCS'03: Proceedings of the 2003 international conference on Computational science: PartII

**Publisher:** Springer-Verlag

The Lanczos algorithm is a well known procedure to compute few eigenvalues of large symmetric matrices. We slightly modify this algorithm in order to obtain the eigenvalues of Hamiltonian matrices H = JS with S symmetric and positive definite. These matrices represent a significant subclass of Hamiltonian matrices since their ...

13

April 2002
ICCS '02: Proceedings of the International Conference on Computational Science-Part III

**Publisher:** Springer-Verlag

We consider the application of symmetric Boundary Value Methods to linear autonomous Hamiltonian systems. The numerical approximation of the Hamiltonian function exhibits a superconvergence property, namely its order of convergence is p + 2 for a p order symmetric method. We exploit this result to define a natural projection procedure ...

14

June 2000
NAA '00: Revised Papers from the Second International Conference on Numerical Analysis and Its Applications

**Publisher:** Springer-Verlag

We investigate interesting spectral properties of circulant matrices with a band structure by analyzing the roots of an associated polynomial. We also derive practical conditions about the curve containing the eigenvalues of the matrix which can be used to study the stability domain of some numerical methods for the solution ...

**Keywords**:
circulant matrices, linear multistep methods, ordinary differential equations

15

October 1998
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany: Volume 28 Issue 2-4, Oct., 1998

**Publisher:** Elsevier Science Publishers B. V.

**Keywords**:
boundary value methods, parallel computers, parallelism across the steps, parallel methods for ODEs

16

December 1997
Journal of Computational and Applied Mathematics: Volume 87 Issue 1, Dec. 1997

**Publisher:** Elsevier Science Publishers B. V.

**Keywords**:
boundary value methods, differential-algebraic equations

17

December 1997
Journal of Computational and Applied Mathematics: Volume 87 Issue 1, Dec. 1997

**Publisher:** Elsevier Science Publishers B. V.

**Keywords**:
implicit methods for ODEs, splittings, modified Newton iteration

18

February 1997
Journal of Computational and Applied Mathematics: Volume 78 Issue 2, Feb. 17, 1997

**Publisher:** Elsevier Science Publishers B. V.

**Keywords**:
parallel computers, boundary value methods, numerical methods for ODEs

19

January 1997
SIAM Journal on Scientific Computing: Volume 18 Issue 1, January. 1997

**Publisher:** Society for Industrial and Applied Mathematics

A parallel algorithm for solving linear systems that arise from the discretization of boundary value ODEs is described. It is a modification of a cyclic reduction algorithm that takes advantage of the almost block diagonal structure of the linear system. A stable modification of the original algorithm is also proposed. ...

**Keywords**:
parallel solvers, ABD systems, boundary value problems

20

June 1996
WNAA '96: Proceedings of the First International Workshop on Numerical Analysis and Its Applications

**Publisher:** Springer-Verlag