The numerical integration of partial differential equations is a particularly difficult task, and there is no generally applicable method. In contrast to ordinary differential equations, the most natural explicit finite difference methods such as replacing differentials by forward, backward, or central finite differences often are numerically unstable, even in the limit of very small discretiza...

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. Keywords—Generalized Rosenau-B...

A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates ε-uniformly convergent numerical approximations to the solution. The method uses a piecewise u...

— In this paper, we are interested in the numerical analysis of blow up for the Chipot-Weissler equation ut = ∆u+ |u| u− |∇u| with Dirichlet boundary conditions in bounded domain when p > 1 and 1 ≤ q ≤ 2p p+ 1 . To approximate the blow up solution, we construct a finite difference scheme and we prove that the numerical solution satisfies the same properties of the exact one and blows up in fini...