TY - JOUR
T1 - The numerical solution of the nonlinear Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method
AU - Shao, Wenting
AU - Wu, Xionghua
N1 - Funding Information:
The support from the National Natural Science Foundation of China under grants (No. 10671146 and No. 50678122 ) is fully acknowledged. The authors are very grateful to the reviewers for carefully reading the paper and for their comments and suggestions which have improved the paper very much.
PY - 2014/5
Y1 - 2014/5
N2 - In this work, we study the numerical solutions of one-dimensional Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method based on the integration-differentiation (CTMMID). First, we apply CTMMID to discretize both space and time variables. The initial and boundary conditions could be incorporated efficiently with full CTMMID. Furthermore, we introduce the Domain Decomposition Method (DDM) in space and the block-marching technique in time for problems defined in large interval and long time computing. The numerical results are more accurate and with less computational effort than some existing studies.
AB - In this work, we study the numerical solutions of one-dimensional Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method based on the integration-differentiation (CTMMID). First, we apply CTMMID to discretize both space and time variables. The initial and boundary conditions could be incorporated efficiently with full CTMMID. Furthermore, we introduce the Domain Decomposition Method (DDM) in space and the block-marching technique in time for problems defined in large interval and long time computing. The numerical results are more accurate and with less computational effort than some existing studies.
KW - Block-marching technique
KW - Chebyshev tau meshless method
KW - Domain Decomposition Method
KW - Integration-differentiation
KW - Klein-Gordon equation
KW - Sine-Gordon equation
UR - http://www.scopus.com/inward/record.url?scp=84900237421&partnerID=8YFLogxK
U2 - 10.1016/j.cpc.2014.02.002
DO - 10.1016/j.cpc.2014.02.002
M3 - Article
AN - SCOPUS:84900237421
SN - 0010-4655
VL - 185
SP - 1399
EP - 1409
JO - Computer Physics Communications
JF - Computer Physics Communications
IS - 5
ER -