Two energy conserving numerical schemes for the sine-Gordon equation
Applied Mathematics and Computation
SIAM Review
Orthogonal cubic spline collocation method for the extended Fisher-Kolmogorov equation
Journal of Computational and Applied Mathematics
Conservative difference methods for the Klein-Gordon-Zakharov equations
Journal of Computational and Applied Mathematics
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Approximate solutions are considered for the extended Fisher-Kolmogorov (EFK) equation in two space dimension with Dirichlet boundary conditions by a Crank-Nicolson type finite difference scheme. A priori bounds are proved using Lyapunov functional. Further, existence, uniqueness and convergence of difference solutions with order O(h^2+k^2) in the L^~-norm are proved. Numerical results are also given in order to check the properties of analytical solutions.