We consider the advection-diffusion equation in one dimension. The equation is solved using an explicit finite difference method. As the method is explicit, it is simple to implement. We investigate the performance of the method. We obtain that the method is indeed accurate.

We propose a staggered-grid finite volume method for solving the shallow water equations involving varying channel width and topography in one dimension. The method is an extension of an existing staggered conservative scheme for shallow water flows. One great advantage of the numerical method is that it does not need any Riemann solver in the flux calculation, so the numerical computation is cheap. We obtain that the method is able to solve a wide range of problems. The proposed method is well balanced and of the first order of accuracy.

Type 2 diabetes mellitus and diabetic foot ulcers remain serious worldwide health problems. Caffeic acid is one of the natural products that has been experimentally proven to have diverse pharmacological properties. This study aimed to assess the inhibitory activity of caffeic acid and ethanolic extract of spent coffee grounds targeting DPP-4 and MMP-9 enzymes and evaluate the molecular interactions through 50-ns molecular dynamics simulations. This study also introduced our new version of PyPLIF HIPPOS, PyPLIF HIPPOS 0.2.0, which allowed us to identify protein–ligand interaction fingerprints and interaction hotspots resulting from molecular dynamics simulations. Our findings revealed that caffeic acid inhibited the DPP-4 and MMP-9 activity with an IC₅₀ of 158.19 ± 11.30 µM and 88.99 ± 3.35 µM while ethanolic extract of spent coffee grounds exhibited an IC₅₀ of 227.87 ± 23.80 µg/100 µL and 81.24 ± 6.46 µg/100 µL, respectively. Molecular dynamics simulations showed that caffeic acid interacted in the plausible allosteric sites of DPP-4 and in the active site of MMP-9. PyPLIF HIPPOS 0.2.0 identified amino acid residues interacting more than 10% throughout the simulation, which were Lys463 and Trp62 in the plausible allosteric site of DPP-4 and His226 in the active site of MMP-9.