A hybrid asymptotic-numerical method is presented for obtaining an asymptotic estimate for
the full probability distribution of capture times of a random walker by multiple small traps …

The dynamics and stability of multispot patterns to the Gray–Scott (GS) reaction-diffusion
model in a two-dimensional domain is studied in the singularly perturbed limit of small …

Among the algorithms that are likely to play a major role in future exascale computing, the
fast multipole method (fmm) appears as a rising star. Our previous recent work showed …

This paper concerns a class of deferred correction methods recently developed for initial
value ordinary differential equations; such methods are based on a Picard integral form of …

The integral equation approach to partial differential equations (PDEs) provides significant
advantages in the numerical solution of the incompressible Navier-Stokes equations. In …

In this paper we consider the modified Helmholtz type equation governing 2D-boundary
value problems for anisotropic functionally graded materials (FGMs) with Dirichlet and …

In this paper, the Cauchy problem of the modified Helmholtz equation (CPMHE) with
perturbed wave number is considered. In the sense of Hadamard, this problem is severely ill …

We present a kernel-independent, adaptive fast multipole method (FMM) of arbitrary order
accuracy for solving elliptic PDEs in three dimensions with radiation and periodic boundary …

A new scheme is presented for imposing periodic boundary conditions on unit cells with
arbitrary source distributions. We restrict our attention here to the Poisson, modified …

Based on the kernel-free boundary integral method proposed by Ying and Henriquez (J
Comput Phys 227 (2): 1046–1074, 2007), which is a second-order accurate method for …