Computing high-order derivatives in compact integrated-RBF stencils

In Mai-Duy and Strunin (Mai-Duy Strunin, 2021), it was shown that the inclusion of nodal values high-order derivatives in compact local integrated-radial-basis-function (IRBF) stencils results a significant improvement solution accuracy. The purpose this work is to examine detail numerical performance several approximation schemes based on one-dimensional IRBFs for computing along grid lines. extended precision floating point arithmetic utilised achieve high level accuracy, efficiencies are improved by employing overlapping domain decomposition mixed-precision calculations. solving partial differential equations (PDEs), proposed 1D-IRBFs implemented using RBF widths fixed vary with refinement. A simple framework presented cover two width cases, analysis carried out problems slow rapid variations their solutions. convection–diffusion equations, also incorporated into upwind effectively simulating highly-nonlinear flows. Numerical show rates convergence respect refinement achieved both variable widths.