Error analysis of method of lines (MOL) via generalized interpolating moving least squares (GIMLS) approximation

This paper gives an error analysis for the method of lines (MOL) using generalized interpolating moving least squares (GIMLS) approximation. In this study, error bound for the time-dependent linear and nonlinear second-order differential equations in d-dimension will be obtained, when the GIMLS method is used for approximating the spatial variables. Also, the well-known Courant-Friedrichs-Lewy (CFL) condition will be derived in both cases (linear and nonlinear equations). Finally, numerical examples will be reported to confirm the ability of the proposed technique.