On the Conservative Finite Difference Scheme for the Generalized Novikov Equation

A Conservative Finite Difference Scheme for Static Diffusion Equation

A new discretization scheme for partial differential equations, based on the finite differences method, and its application to the two dimensional static diffusion equation is presented. This scheme produces better approximations than a standard use of finite differences. It satisfies properties of continuous differential operators and discrete versions of integral identities, which guarantee i...

The new implicit finite difference scheme for two-sided space-time fractional partial differential equation

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

Two Conservative Difference Schemes for the Generalized Rosenau Equation

Conservative finite difference schemes for the Degasperis-Procesi equation

We consider the numerical integration of the Degasperis–Procesi equation, which was recently introduced as a completely integrable shallow water equation. For the equation, we propose nonlinear and linear finite difference schemes that preserve two invariants associated with the bi-Hamiltonian form of the equation at a same time. We also prove the unique solvability of the schemes, and show som...

Crank-Nicolson Difference Scheme for the Generalized Rosenau-Burgers Equation

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...