Numerical Solution for Super Large Scale Systems

Author

Tianmin Han ; Yuhuan Han

Author_Institution

China Electr. Power Res. Inst., Beijing, China

Volume

1

fYear

2013

fDate

2013

Firstpage

537

Lastpage

544

Abstract

In this paper, a new ordinary differential equation numerical integration method is successfully applied to various mathematical branches such as partial differential equation (PDE) boundary problems, PDE initial-boundary problems, tough nonlinear equations, and so forth. The new method does not use Jacobian, so it can handle very large systems, say the dimension N=1 000 000, or even larger. In addition, we give a very simple accelerating convergence approach for the linear algebraic equations arising from linear PDE boundary problems. All the numerical results show that the new method is very promising for super large scale systems.

Keywords

initial value problems; partial differential equations; Jacobian; PDE boundary problem; PDE initial boundary problem; numerical integration method; ordinary differential equation; partial differential equation; super large scale systems; tough nonlinear equations; Differential equations; Jacobian matrices; Large-scale systems; Mathematical model; Nonlinear equations; Numerical stability; Stability analysis; GMRES(m); ODE method; PDE boundary problem; Super large scale systems; inexact Newton method; linear equations; nonlinear equations; numerical solution; parallel computation;

fLanguage

English

Journal_Title

Access, IEEE

Publisher

ieee

ISSN

2169-3536

Type

jour

DOI

10.1109/ACCESS.2013.2280244

Filename

6588290