On Convergence of Iterative Methods for a Fourth-Order Discretization Scheme

Fourth-order numerical solution of a fractional PDE with the nonlinear source term in the electroanalytical chemistry

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

On Convergence of Iterative Methods for a Fourth-Order Discretization Scheme

Solving systems of nonlinear equations using decomposition technique

A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of Newton multi-step method. The auxiliary function provides us the way to overcome the singul...

A note on convergence of line iterative methods for a nine-point matrix

We prove the convergence of line iterative methods for solving the linear system arising from a 9-point compact discretization of a special two dimensional convection-diiusion equation. The results provide rigorous justiication for the numerical experiments conducted elsewhere, which demonstrate the high accuracy and stability advantages of the fourth-order compact scheme.

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence