This paper focuses on a new framework for obtaining a nonintrusive (ie, not requiring
projecting of the governing equations onto the reduced basis modes) reduced order model …

In this paper it is shown the application of the generalized finite difference method (GFDM)
for solving numerically the Telegraph equation in two and three-dimensional spaces. The …

Abstract The Klein–Gordon equation with nonlinear potential occurs in a wide range of
application areas in science and engineering. Its computation represents a major challenge …

By the rapid growth of available data, providing data‐driven solutions for nonlinear
(fractional) dynamical systems becomes more important than before. In this paper, a new …

The main aim of present work is to develop the two meshless collocation methods based on
radial basis function-generated finite difference (RBF-FD) and global RBF (GRBF) methods …

In this paper we explore arbitrarily high-order Lagrange collocation-type time-stepping
schemes for effectively solving high-dimensional nonlinear Klein–Gordon equations with …

Recently, the numerical methods for long‐time dynamics of PDEs with weak nonlinearity (or
small potentials) have received more and more attention. For the Klein‐Gordon‐Dirac (KGD) …

The present study is influenced by the wide applications of the Schrödinger equations. Its
occurrence can be easily seen in electromagnetic wave propagation, quantum mechanics …

In this paper, a localized meshless collocation method, the generalized finite difference
method (GFDM), is first applied to calculate the bandgaps of anti-plane transverse elastic …

We apply a numerical scheme based on a meshless method in space and an explicit
exponential Runge-Kutta in time for the solution of the damped Kuramoto–Sivashinsky …