Increased attention has been paid on numerical modeling of interface problems as its wide
applications in various aspects of science. Motivated by enhancing the application of the …

A new augmented method is proposed for elliptic interface problems with a piecewise
variable coefficient that has a finite jump across a smooth interface. The main motivation is to …

When thermal diffusivity does not vary smoothly within a computational domain, standard
numerical methods for solving heat equilibrium problems often converge to an inaccurate …

In this paper, the difference potentials method-based ADI finite difference scheme is
proposed for numerical solutions of two-dimensional nonlinear convection–diffusion …

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

We present a robust and effective method for the numerical solution of the biharmonic
interface problem with discontinuities in both the solution and its derivatives. We use a …

In this paper, an efficient numerical method is proposed for the 1D elliptic type interface
problems. We first construct a broken reproducing kernel space and then apply the …

In this work, we discuss and compare three methods for the numerical approximation of
constant-and variable-coefficient diffusion equations in both single and composite domains …

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

In this paper, we present a robust and accurate numerical algorithm for solving the nonlinear
Poisson–Boltzmann equation, based on the difference potentials method (DPM). First, we …