Local meshless method for PDEs arising from models of wound healing

Abstract

• In this work a local meshless procedure is developed for PDEs arising from wound healing models. • An upwind technique is incorporated in the meshless procedure. • Uniform and non-uniform nodal distributions are considered on regular and irregular geometries. • Different wound healing models with and without hyperbaric oxygen therapy are simulated. • Some useful conclusions are drawn about the acute and chronic wounds healing processes. A meshless collocation procedure is proposed for one- and two-dimensional partial differential equations arising from modeling of wound healing processes (Sherratt and Murray, 1991). Main motivation of this choice is its straightforward application in higher dimensions for both regular and irregular domains on various nodal points distributions. In the case of numerical solution of convection-dominated wound healing PDE models, a stencil based upwind stabilization technique is coupled with the local meshless method to counter instabilities of the computed solution. To assess efficacy, efficiency and accuracy of the proposed method on regular and irregular domains, numerical approximations of different wound healing models are obtained and validated against the exact solution and medically tested healing time duration.