Modified HPMs Inspired by Homotopy Continuation Methods

摘要

Nonlinear differential equations have applications in the modelling area for a broad variety of phenomenaand physical processes; having applications for all areas in science and engineering. At the presenttime, the homotopy perturbation method (HPM) is amply used to solve in an approximate or exact mannersuch nonlinear differential equations. This method has found wide acceptance for its versatility and easeof use. The origin of the HPM is found in the coupling of homotopy methods with perturbationmethods. Homotopy methods are a well established research area with applications, in particular, an appliedbranch of such methods are the homotopy continuation methods, which are employed on the numericalsolution of nonlinear algebraic equation systems. Therefore, this paper presents two modified versions ofstandard HPM method inspired in homotopy continuation methods. Both modified HPMs dealwith nonlinearities distribution of the nonlinear differential equation. Besides, we will use a calcium-inducedcalcium released mechanism model as study case to test the proposed techniques. Finally, resultswill be discussed and possible research lines will be proposed using this work as a starting point.