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Numerical methods for the extended Fisher-Kolmogorov (EFK) equation. (English) Zbl 1111.65085
The authors prove the existence, uniqueness and regularity properties for the extended Fisher-Kolmogorov equation. The semidiscrete Galerkin method using C 1 -conforming finite elements, fully discrete schemes like backward Euler, two step backward difference and Crank-Nicolson methods are proposed and studied. Optimal error estimates for these methods are derived.
MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M20Method of lines (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
35Q72Other PDE from mechanics (MSC2000)
65M15Error bounds (IVP of PDE)