Spatial–temporal calcium dynamics due to calcium release, buffering and re-uptaking plays a central role in studying excitation–contraction (E–C) coupling in both normal and diseased cardiac myocytes. In this paper, we employ a meshless method, namely, the local radial basis function collocation method (LRBFCM), to model such calcium behaviors by solving a nonlinear system of reaction–diffusion...

In this study, we use an effective meshless method to estimate the numerical solution of 3-D time-fractional Sobolev equation. The recommended is used for spatial derivatives while Liouville-Caputo derivative technique utilized time portion model Accuracy assessed via error norms and comparison made with exact other methods given in more current literature, which demonstrated that suggested str...

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of i...

Here are three short stories on meshless methods using kernel techniques: • Any well–posed linear problem in the native space NΦ of a symmetric (strictly) positive definite kernel Φ can be successfully solved by symmetric meshless collocation. This applies to a large variety of standard linear PDE problems. • Relaxing interpolation conditions by allowing some small absolute error can significan...

Abstract: A meshless method based on radial point interpolation was recently developed as an effective tool for solving partial differential equations, and has been widely applied to a number of different problems. In addition to the primary advantage of the meshless methods that the computation is performed without any connectivity information between field nodes, the radial point interpolatio...

We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the threedimensional analysis of the pr...

The paper deals with the numerical solution of initial-boundary value problems for diffusion equation with variable coefficients by using a local weak formulation and a meshless approximation of spatial variations of the field variable. The time variation is treated either by the Laplace transform technique or by the linear Lagrange interpolation in the time stepping approach. Advanced formulat...

A truly Meshless Local Petrov-Galerkin (MLPG) method is developed for solving 3D elasto-static problems. Using the general MLPG concept, this method is derived through the local weak forms of the equilibrium equations, by using a test function, namely, the Heaviside step function. The Moving Least Squares (MLS) are chosen to construct the shape functions. The penalty approach is used to impose ...

Development of a new meshless technique is described, called the meshless volume scheme. The method is completely meshless, yet retains the low storage and simple flux distribution technique characteristic of finite volume methods. The new method is based on the well-known Taylor series expansion method with least squares. A least squares weighting scheme is introduced that significantly reduce...