...Hamid Mesgarani; Mahya Kermani; Mostafa Abbaszadeh Purpose The purpose of this study is to use the method of lines to solve the two-dimensional nonlinear advection–diffusion–reaction equation with variable coefficients. Design/methodology/approach The strictly positive definite radial basis...

...J.I. Ramos Purpose The purpose of this study is to develop a new method of lines for one-dimensional (1D) advection-reaction-diffusion (ADR) equations that is conservative and provides piecewise analytical solutions in space, compare it with other finite-difference discretizations and assess...

... the numerical method. Section 5 is devoted to the numerical experiments on two benchmark problems with Dirichlet and Neumann boundary conditions. The last section is a brief conclusion. Local meshless method Burgers’ equations Method of lines Newton basis functions Reproducing Kernel Hilbert space...

...Syed Tauseef Mohyud‐Din; Elham Negahdary; Muhammad Usman Purpose The purpose of this paper is to present a numerical solution of a family of generalized fifth‐order Korteweg‐de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives...