Orthogonal cubic spline collocation method for the extended Fisher–Kolmogorov equation

A second-order splitting combined with orthogonal cubic spline collocation method is formulated and analysed for the extended Fisher–Kolmogorov equation. With the help of Lyapunov functional, a bound in maximum norm is derived for the semidiscrete solution. Optimal error estimates are established fo...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2005-02, Vol.174 (1), p.101-117
Main Authors: Danumjaya, P., Pani, Amiya K.
Format: Article
Language:English
Subjects:
A priori bounds
Exact sciences and technology
Extended Fisher–Kolmogorov (EFK) equation
Fourier analysis
Gaussian quadrature rule
Lyapunov functional
Mathematical analysis
Mathematics
Monomial basis functions
Numerical analysis
Numerical analysis. Scientific computation
Optimal order of convergence
Ordinary differential equations
Orthogonal cubic spline collocation method
RADAU 5
Sciences and techniques of general use
Second-order splitting
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Summary:A second-order splitting combined with orthogonal cubic spline collocation method is formulated and analysed for the extended Fisher–Kolmogorov equation. With the help of Lyapunov functional, a bound in maximum norm is derived for the semidiscrete solution. Optimal error estimates are established for the semidiscrete case. Finally, using the monomial basis functions we present the numerical results in which the integration in time is performed using RADAU 5 software library.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2004.04.002