TY - JOUR
T1 - Numerical study of Fisher's reaction-diffusion equation by the Sinc collocation method
AU - Al-Khaled, Kamel
PY - 2001/12/15
Y1 - 2001/12/15
N2 - Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by the Sinc collocation method. The derivatives and integrals are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The error in the approximation of the solution is shown to converge at an exponential rate. Numerical examples are given to illustrate the accuracy and the implementation of the method, the results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are independent of the initial values.
AB - Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by the Sinc collocation method. The derivatives and integrals are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The error in the approximation of the solution is shown to converge at an exponential rate. Numerical examples are given to illustrate the accuracy and the implementation of the method, the results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are independent of the initial values.
KW - Fisher's equation
KW - Nonlinear parabolic equation
KW - Reaction-diffusion equations
UR - http://www.scopus.com/inward/record.url?scp=0035892569&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035892569&partnerID=8YFLogxK
U2 - 10.1016/S0377-0427(01)00356-9
DO - 10.1016/S0377-0427(01)00356-9
M3 - Article
AN - SCOPUS:0035892569
SN - 0377-0427
VL - 137
SP - 245
EP - 255
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -