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research article

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Hao, Wenrui
•
Hesthaven, Jan  
•
Lin, Guang
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January 13, 2020
Journal Of Scientific Computing

The homotopy continuation method has been widely used to compute multiple solutions of nonlinear differential equations, but the computational cost grows exponentially based on the traditional finite difference and finite element discretizations. In this work, we presented a new method by constructing a spectral approximation space adaptively based on a greedy algorithm for nonlinear differential equations. Then multiple solutions were computed by the homotopy continuation method on this low-dimensional approximation space. Various numerical examples were given to illustrate the feasibility and the efficiency of this new approach.

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Type
research article
DOI
10.1007/s10915-020-01123-1
Web of Science ID

WOS:000513923900002

Author(s)
Hao, Wenrui
•
Hesthaven, Jan  
•
Lin, Guang
•
Zheng, Bin
Date Issued

2020-01-13

Publisher

SPRINGER/PLENUM PUBLISHERS

Published in
Journal Of Scientific Computing
Volume

82

Issue

1

Start page

19

Subjects

Mathematics, Applied

•

Mathematics

•

multiple solutions

•

nonlinear differential equations

•

polynomial systems

•

homotopy continuation

•

free-boundary problems

•

mathematical-model

•

tumor-growth

•

bifurcation

•

continuation

•

stability

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
MCSS  
Available on Infoscience
March 5, 2020
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/167009
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