A Theoretical Introduction to Numerical Analysis presents the general methodology and
principles of numerical analysis, illustrating these concepts using numerical methods from …

The method of difference potentials was originally proposed by Ryaben'kii and can be
interpreted as a generalized discrete version of the method of Calderon's operators in the …

We describe a high-order accurate methodology for the numerical simulation of time-
harmonic waves governed by the Helmholtz equation. Our approach combines compact …

In the present paper, we consider active control of noise propagating from a long cylinder.
For that purpose control sources are distributed on the external surface of the cylinder. They …

Numerical approximations and modeling of many physical, biological, and biomedical
problems often deal with equations with highly varying coefficients, heterogeneous models …

For a class of linear constant-coefficient finite-difference operators of the second order, we
introduce the concepts similar to those of conventional single-and double-layer potentials for …

The method of difference potentials generalizes the method of Calderon's operators from
PDEs to arbitrary difference equations and systems. It offers several key advantages, such …

Calderón–Ryaben'kii potentials provide the foundation for the difference potential method,
which is an efficient way for solving boundary-value problems (BVPs) in arbitrary domains …

Highly-accurate numerical methods that can efficiently handle problems with interfaces
and/or problems in domains with complex geometry are crucial for the resolution of different …

Numerical approximations and computational modeling of problems from Biology and
Materials Science often deal with partial differential equations with varying coefficients and …