Skip to content
Home
About Us
Resources
Profiles Metrics
Authors Directory
Institutions Directory
Top Authors
Top Institutions
Top Sponsors
AI Digest
Contact Us
Menu
Home
About Us
Resources
Profiles Metrics
Authors Directory
Institutions Directory
Top Authors
Top Institutions
Top Sponsors
AI Digest
Contact Us
Home
About Us
Resources
Profiles Metrics
Authors Directory
Institutions Directory
Top Authors
Top Institutions
Top Sponsors
AI Digest
Contact Us
Menu
Home
About Us
Resources
Profiles Metrics
Authors Directory
Institutions Directory
Top Authors
Top Institutions
Top Sponsors
AI Digest
Contact Us
Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
mathematics
Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs
Journal of Symbolic Computation, Volume 37, No. 6, Year 2004
Notification
URL copied to clipboard!
Description
Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi's elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi's sn or cn functions. Examples illustrate key steps of the algorithms. The new algorithms are implemented in Mathematica. The package PDESpecialSolutions.m can be used to automatically compute new special solutions of nonlinear PDEs. Use of the package, implementation issues, scope, limitations, and future extensions of the software are addressed. A survey is given of related algorithms and symbolic software to compute exact solutions of nonlinear differential equations. © 2004 Elsevier Ltd. All rights reserved.
Authors & Co-Authors
Baldwin, D.
United States, Golden
Colorado School of Mines
Göktaş, Ü
United States, Urbana-champaign
Wolfram Research, Inc.
Hereman, Willy A.
United States, Golden
Colorado School of Mines
South Africa, Stellenbosch
Stellenbosch University
Hong, L.
United States, Cambridge
Harvard University
Martino, R. S.
United States, Golden
Colorado School of Mines
Miller, Joel C.
United Kingdom, Cambridge
Churchill College
Statistics
Citations: 171
Authors: 6
Affiliations: 5
Identifiers
Doi:
10.1016/j.jsc.2003.09.004
ISSN:
07477171
Study Design
Cross Sectional Study
Study Approach
Quantitative