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 …

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

We solve the wave equation with variable wave speed on nonconforming domains with
fourth order accuracy in both space and time. This is accomplished using an implicit finite …

In this paper, an h∕ p spectral element method with least-square formulation for parabolic
interface problem will be presented. The regularity result of the parabolic interface problem …

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

We consider interior and exterior initial boundary value problems for the three-dimensional
wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator …

Designing numerical methods with high-order accuracy for problems in irregular domains
and/or with interfaces is crucial for the accurate solution of many problems with physical and …

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 …

Two new numerical methods based on Haar wavelet collocation and meshless collocation
are proposed for solution of parabolic type of time marching interface models. This work is …

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 …