Force-velocity-power (FVP) profiling offers insights related to key factors that may enhance or hinder sprinting performances. Whether the same FVP principles could be applied to the sprinting portion of the 3-minute all-out test for running (3MT) has not been previously investigated. Twenty moderately trained participants volunteered for the study (age: 24.75 ± 3.58 yrs; height: 1.69±0.11 m; mass: 73.74±12.26 kg). After familiarization of all testing procedures, participants completed: (i) a 40-m all-out sprint test, and (ii) a 3MT. Theoretical maximal force and power, but not velocity, were significantly higher for the 40-m sprint test. Most FVP variables from the two tests were weakly to moderately correlated, with the exception of maximal velocity. Finally, maximal velocity and relative peak power were predictive of D’, explaining approximately 51% of the variance in D’. Although similar maximal velocities are attained during both the 40-m sprint and the 3MT, the underlying mechanisms are markedly different. The FVP parameters obtained from either test are likely not interchangeable but do provide valuable insights regarding the potential mechanisms by which D’ may be improved.

The paper discusses the numerical solution of the one-dimensional radially axi-symmetric non-linear second-order differential equation to model the conduction and radiation transfer through a spherical domain as a result of an exothermic heat source. The equation is transformed to a non-dimensional form. The dimensionless numbers emanating from the transformation represent the effect of the reaction rate, reaction type, activation energy, radiation and the convection on the temperature. The non-dimensional differential equation for the temperature distribution was previously solved using the Runge-Kutta-Fehlberg method coupled with a Shooting technique. In this paper the solution of the non-dimensional differential equation using an iterative Galerkin finite element method approach employing the Picard method is described. The commercial finite element code Comsol is also employed to solve the non-dimensional differential equation. The current study was motivated by inconsistencies that were observed in the previous results that were presented. Although the assumed underlying physics is used to evaluate the results, the study focuses purely on the numerical solution of the non-dimensional differential equation. The results obtained by the Galerkin finite element code and Comsol were found to be in exact agreement and also exhibit no inconsistencies.

Two standard and two nonstandard finite difference schemes are constructed to solve a basic reaction–diffusion–chemotaxis model, for which no exact solution is known. The continuous model involves a system of nonlinear coupled partial differential equations subject to some specified initial and boundary conditions. It is not possible to obtain theoretically the stability region of the two standard finite difference schemes. Through running some numerical experiments, we deduce heuristically that these classical methods give reasonable solutions when the temporal step size k k is chosen such that k ≤ 0.25 k\le 0.25 with the spatial step size h h fixed at h = 1.0 h=1.0 (first novelty of this work). We observe that the standard finite difference schemes are not always positivity preserving, and this is why we consider nonstandard finite difference schemes. Two nonstandard methods abbreviated as NSFD1 and NSFD2 from Chapwanya et al. are considered. NSFD1 was not used by Chapwanya et al. to generate results for the basic reaction–diffusion–chemotaxis model. We find that NSFD1 preserves positivity of the continuous model if some criteria are satisfied, namely, ϕ ( k ) [ ψ ( h ) ] 2 = 1 2 γ ≤ 1 2 σ + β \frac{\phi \left(k)}{{\left[\psi \left(h)]}^{2}}=\frac{1}{2\gamma }\le \frac{1}{2\sigma +\beta } and β ≤ σ \beta \le \sigma , and this is the second novelty of this work. Chapwanya et al. modified NSFD1 to obtain NSFD2, which is positivity preserving if R = ϕ ( k ) [ ψ ( h ) ] 2 = 1 2 γ R=\frac{\phi \left(k)}{{\left[\psi \left(h)]}^{2}}=\frac{1}{2\gamma } and 2 σ R ≤ 1 2\sigma R\le 1 , that is σ ≤ γ \sigma \le \gamma , and they presented some results. For the third highlight of this work, we show that NSFD2 is not always consistent and prove that consistency can be achieved if β → 0 \beta \to 0 and k h 2 → 0 \frac{k}{{h}^{2}}\to 0 . Fourthly, we show numerically that the rate of convergence in time of the four methods for case 2 is approximately one.

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