Linearized stability analysis of discrete Volterra equations

Boundedness and stability of discrete Volterra equations

Discrete Collocation Method for Solving Fredholm Volterra Intergro-Differential Equations

Periodic solutions of discrete Volterra equations

In this paper, we investigate periodic solutions of linear and nonlinear discrete Volterra equations of convolution or non-convolution type with unbounded memory. For linear discrete Volterra equations of convolution type, we establish Fredholm’s alternative theorem and for equations of non-convolution type, and we prove that a unique periodic solution exists for a particular bounded initial fu...

Preconditioners for Linearized Discrete Compressible Euler Equations

We consider a Newton-Krylov approach for discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is essential for obtaining an efficient solver in such an approach. In this paper we compare point-block-Gauss-Seidel, point-block-ILU and point-block-SPAI preconditioners. It turns out that the SPAI method is not satisfactory for our problem class. The point-bl...

Discrete Volterra Equations - Discrete Volterra Operators, Fixed Point Theorems & their Application