The occurrences of differential equations and integral equations are common in many areas of studies in particular sciences and engineering. However, there are many mathematical formulations in ...

Abstract: For modelling large-scale 3-D scalar-wave propagation, the finite-difference (FD) method with high-order accuracy in space but second-order accuracy in time is widely used because of its ...

In the practical problems such as nuclear waste pollution and seawater intrusion etc., many problems are reduced to solving the convection-diffusion equation, so the research of convection-diffusion ...

Abstract: This paper presents an upwind finite-difference method for the numerical approximation of viscosity solutions of a Hamilton-Jacobi-Bellman (HJB) equation governing a class of optimal ...

Implementation of gauged string method for the calculation of minimum energy path of vortex nucleation in superconductors within Ginzburg-Landau theory.