Abstract: In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.
Abstract: A new nonlinear sum-difference inequality in two variables
which generalize some existing results and can be used as handy
tools in the analysis of certain partial difference equation is discussed.
An example to show boundedness of solutions of a difference value
problem is also given.