Some biomechanical models are represented by nonlinear first order ordinary differential equations. The objective of this study is to determine the velocity of a biomechanical model that involves a cyclist coasting downhill. Two methods namely; the modified explicit and diagonally implicit fifth–order Runge–Kutta methods are utilised. The performance of the two methods is compared with the exac...

In this note we propose and analyze an implicit-explicit scheme based on second order strong stability preserving time discretisations. We also present some theoretical and numerical stability results for second order Runge Kutta IMEX schemes.

Abstract In this work, a version of continuous stage stochastic Runge–Kutta (CSSRK) methods is developed for differential equations (SDEs). First, general order theory these established by the B-series and multicolored rooted tree. Then proposed CSSRK are applied to three special kinds SDEs corresponding conditions derived. particular, single integrand with additive noise, we construct some spe...