PREM：并行求解非线性演化方程行波解的软件包

doi:10.3969/j.issn.1000-5641.2017.04.002

华东师范大学学报(自然科学版) ›› 2017, Vol. ›› Issue (4): 18-33.doi: 10.3969/j.issn.1000-5641.2017.04.002

PREM：并行求解非线性演化方程行波解的软件包

张治安, 柳银萍

华东师范大学计算机科学与技术系, 上海 200062

收稿日期:2016-09-28 出版日期:2017-07-25 发布日期:2017-07-20
通讯作者: 柳银萍,女,教授,研究方向为符号计算.E-mail:ypliu@cs.ecnu.edu.cn. E-mail:ypliu@cs.ecnu.edu.cn
作者简介:张治安,男,硕士研究生,研究方向为数学机械化.E-mail:yifanzza@163.com.
基金资助:
国家自然科学基金（11435005）

PREM: A parallel package for finding travelling wave solutions to nonlinear evolution equations

ZHANG Zhi-an, LIU Yin-ping

Department of Computer Science and Technology, East China Normal University, Shanghai 200062, China

Received:2016-09-28 Online:2017-07-25 Published:2017-07-20

摘要/Abstract

摘要： 本文提出了一种新的构造非线性演化方程行波解的并行算法.我们在Maple 18上实现了该算法.通过设计并行算法并使用负载均衡技术，其中的软件PREM的计算效率明显高于已有的串行软件.且基于因式分解算法和运行时间限制，PREM可以自动推导出一些串行程序算不动的复杂方程的部分精确解.相比于已有的其他程序，PREM可自动推导出更多类型的精确行波解.此外，PREM具有灵活的接口和输出.

关键词: 非线性演化方程, 行波解, Riccati 方程方法, 并行算法, 负载均衡

Abstract: In this paper, a new parallel algorithm and its implementation called PREM for solving nonlinear evolution equations are presented. PREM is developed in Maple 18. By using parallel and load balancing techniques, PREM is more efficient than any previous serial programs. Furthermore, for some complicated equations that serial programs failed to solve, PREM may obtain some exact traveling wave solutions by factoring algorithm and time limit. In addition, the interface and output of PREM is flexible and diverse. More types of exact travelling wave solutions could be obtained by using this parallel program.

Key words: nonlinear evolution equation, travelling wave solutions, Riccati equations methods, parallel algorithm, load balance

中图分类号:

TP311.1

张治安, 柳银萍. PREM：并行求解非线性演化方程行波解的软件包[J]. 华东师范大学学报(自然科学版), 2017, (4): 18-33.

ZHANG Zhi-an, LIU Yin-ping. PREM: A parallel package for finding travelling wave solutions to nonlinear evolution equations[J]. Journal of East China Normal University(Natural Sc, 2017, (4): 18-33.

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PREM：并行求解非线性演化方程行波解的软件包

PREM: A parallel package for finding travelling wave solutions to nonlinear evolution equations

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