The Ginzburg–Landau equation has been used as a mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study the complex Ginzburg–Landau equation in two spatial dimensions with periodical boundary conditions. The method numerically approximates the solution by collocation method based on radial basis functions (RBFs). To improve the numer...

This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery problems for functions from their data. Well-posedness of the problem means that this recovery is continuous. Discretization recovers restricted trial functions from restricted test data, and it is well-posed or stable, ...

Meshfree particle method, which is always regarded as a pure Lagrangian approach, is easily represented complicated domain topologies, moving boundaries, and multiphase media. Solving acoustic problems with the mesfree particle method forms a branch of the acoustic wave modeling field, namely, particle-based computational acoustics (PCA). The aim of this paper is to improve the accuracy of usin...

ii Preface Radial Basis Function (RBF) methods have become the primary tool for interpolating multidimensional scattered data. RBF methods also have become important tools for solving Partial Differential Equations (PDEs) in complexly shaped domains. Classical methods for the numerical solution of PDEs (finite difference, finite element, finite volume, and pseudospectral methods) are based on p...

this article deals with the buckling analysis of perfectly bonded cross-ply laminated composite plates reinforced by wavy carbon nanotubes (cnts) under in-plane loads using element free galerkin (efg) method based on first-order shear deformation theory (fsdt). the wavy single-walled cnts and poly-co-vinylene are used for the fibers and the matrix, respectively. the cnt fibers are distributed i...

Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that operators are commonly associated with volume constrained conditions. Moreover, application Fourier and Laplace transforms, which essential majority available methods ABCs, complicated. In this paper, we propose a simple method construct accurate ABCs peridynamic sca...

For thin plate problems, using the Kirchoff hypothesis, the three dimensional elasticity equations are reduced to a fourth order PDE for the vertical displacement. Conventional FEM has difficulties with this because the basis functions are required to have continuous partial derivatives. Meshfree methods have the advantage of constructing smooth approximation functions, but have difficulties in...

Abstract. In this paper, shallow water equations (SWE) are solved through a variety of meshless methods known as radial basis functions (RBF) methods. RBF based Meshless methods have gained much attention in recent years for both the mathematics as well as the engineering community. They have been extensively popularized owing to their flexibility, power and simplicity in solving partial differ...

This paper presents a new approach based on the meshless local Petrov–Galerkin (MLPG) and collocation methods to treat the parabolic partial differential equations with non-classical boundary conditions. In the presented method, the MLPG method is applied to the interior nodes while the meshless collocation method is applied to the nodes on the boundaries, and so the Dirichlet boundary conditio...