Numerical algorithm research for nonlinear ODEs and stability analysis in computer

Author

Peng, Yamian ; Yang, Aimin ; Chang, Jincai ; Gong, Dianxuan ; Zheng, Shiqiu

Author_Institution

Coll. of Sci., Hebei Polytech. Univ., Tangshan, China

Volume

2

fYear

2009

fDate

5-6 Dec. 2009

Firstpage

168

Lastpage

171

Abstract

This paper discussed numerical algorithm of the initial and boundary value problem of nonlinear ordinary differential equations and analysis its stability in computer. The iterated algorithm with spline function for initial value problem in nonlinear ordinary differential equations was studied. Based on the principle of Newton´s algorithm for nonlinear equation, a parallel algorithm for initial value problems in nonlinear ordinary differential equations is constructed and then analysis the stability of this method. It shows that the methods have high precision and quick convergence speed and good stability.

Keywords

initial value problems; iterative methods; nonlinear differential equations; numerical stability; parallel algorithms; splines (mathematics); Newton algorithm; boundary value problem; convergence; initial value problem; iterated algorithm; nonlinear ODE; nonlinear equation; nonlinear ordinary differential equations; numerical algorithm; parallel algorithm; spline function; stability analysis; Acoustic distortion; Algorithm design and analysis; Boundary value problems; Circuits; Differential equations; Diodes; Gears; Nonlinear distortion; Spline; Stability analysis; nonlinear ODEs; numerical continuation method; the initial and boundary value problem; the iterated algorithm with spline function;

fLanguage

English

Publisher

ieee

Conference_Titel

Test and Measurement, 2009. ICTM '09. International Conference on

Conference_Location

Hong Kong

Print_ISBN

978-1-4244-4699-5

Type

conf

DOI

10.1109/ICTM.2009.5413085

Filename

5413085