In this paper we construct fundamental solutions of a scalar conservation law in one space dimension. These source-type solutions are well known for a convex case and hence our focus is on a general non-convex case which may have a finite number of inflection points. Signed fundamental solutions are constructed first and then under an extra hypothesis on nonnegativity of the flux two parameter ...

In this article we describe a numerical method to solve a nonhomogeneous diffusion equation with arbitrary geometry by combining the method of fundamental solutions (MFS), the method of particular solutions (MPS), and the eigenfunction expansion method (EEM). This forms a meshless numerical scheme of the MFS-MPS-EEM model to solve nonhomogeneous diffusion equations with time-independent source ...

This paper has made some significant advances in the boundary-only and domain-type RBF techniques. The proposed boundary knot method (BKM) is different from the standard boundary element method in a number of important aspects. Namely, it is truly meshless, exponential convergence, integration-free (of course, no singular integration), boundary-only for general problems, and leads to symmetric ...

In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...

In this work we show the application of the Method of Fundamental Solutions (MFS) in the determination of eigenfrequencies and eigenmodes associated to wave scattering problems. This meshless method has already been applied to simple geometry domains with Dirichlet boundary conditions (e.g. [8]). Here we show that a particular choice of point-sources can lead to very good results for a fairly g...

In this paper, we employ the regularized meshless method to solve antiplane shear problems with multiple inclusions. The solution is represented by a distribution of double-layer potentials. The singularities of kernels are regularized by using a subtracting and adding-back technique. Therefore, the troublesome singularity in the method of fundamental solutions (MFS) is avoided and the diagonal...

After the successful applications of the combination of the method of fundamental solutions (MFS), the method of particular solutions (MPS), and the eigenfunctions expansion method (EEM) to solve 2D homogeneous and nonhomogeneous diffusion equations by Young et al. (Young et al., Numer Meth Part Differ Equat 22 (2006), 1173), this article intends to extend the same fundamental concepts to calcu...