Arc-Length Method for Differential Equations

Wu Jike; W H Hui; Ding Hongli

Volume 20 Issue 8

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Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(8): 875-880

GUO Yan, LIU Ru-xun. Characteristic-Based Finite Volume Scheme for 1D Euler Equations[J]. Applied Mathematics and Mechanics, 2009, 30(3): 291-300.

Citation:

Wu Jike, W H Hui, Ding Hongli. Arc-Length Method for Differential Equations[J]. Applied Mathematics and Mechanics, 1999, 20(8): 875-880.

GUO Yan, LIU Ru-xun. Characteristic-Based Finite Volume Scheme for 1D Euler Equations[J]. Applied Mathematics and Mechanics, 2009, 30(3): 291-300.

Citation:

Wu Jike, W H Hui, Ding Hongli. Arc-Length Method for Differential Equations[J]. Applied Mathematics and Mechanics, 1999, 20(8): 875-880.

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Arc-Length Method for Differential Equations

1.
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China;
2.
Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, P. R. China

Received Date: 1998-04-20
Rev Recd Date: 1999-02-14
Publish Date: 1999-08-15

Abstract

Abstract

A kind arc-length method is presented to solve the ordinary differential equations(ODEs) with certain types of singularit y as stiff property or discontinuity on continuum problem. By introducing one or two arc-length parameters as variables, the differential equations with singularity are transformed into non-singularity equations, which can be solved by usual methods. The method is also applicable for partial differential equations(PDEs), because they may be changed into systems of ODEs by discretization. Two examples are given to show the accuracy, efficiency and application.
- differential equation,
- numerical method,
- arc-length method,
- stiff equation,
- Burgers’ equation

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References(6)

References

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