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Two new difference schemes are proposed for an initial-boundary-value problem of the Klein-Gordon-Zakharov (KGZ) equations. They have the advantage that there is a discrete energy which is conserved. Their stability and convergence of difference solutions are proved in order O(h² + τ²) on the basis of the prior estimates. Results of numerical experiments demonstrate the efficiency of the new schemes. [ABSTRACT FROM AUTHOR]

Numerical solutions for the general Rosenau-RLW equation are considered and an energy conservative linearized finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence, and a priori error estimate of the scheme are proved using energy method. Numerical results demonstrate that the scheme is efficient and reliable. [ABSTRACT FROM AUTHOR]

A long elastomer with rectangular section bonded between two parallel rigid surfaces will come about deformation because of the role of two opposite shear forces in both the top and bottom plate. The mathematic model of the deformation is deduced and a new difference solving process is proposed. For boundary condition with singularity, a detailed analysis and deduction is given and a new rational and effective discrete boundary condition is proposed. Simulate computation demonstrates that the result is identical with qualitative analysis. Therefore, a new and functional numerical method and quantitative analysis method are provided. [ABSTRACT FROM AUTHOR]

The multi-step backward difference formulas of order k (BDF-k) for 3 ≤ k ≤ 5 are proposed for solving the extended Fisher--Kolmogorov equation. Based upon the careful discrete gradient structures of the BDF-k formulas, the suggested numerical schemes are proved to preserve the energy dissipation laws at the discrete levels. The maximum norm priori estimate of the numerical solution is established by means of the energy stable property. With the help of discrete orthogonal convolution kernels techniques, the L2 norm error estimates of the implicit BDF-k schemes are established. Several numerical experiments are included to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]