Initial Value Methods for the Numerical Simulation of Fuzzy Two-Point Boundary Value Problems Using General Linear Method

This article considers the numerical simulation of fuzzy two-point boundary value problems (FBVP) using general linear method (GLM). The author derived the method, which is a combination of a Runge-Kutta type method and multi-step method. It is originally designed to solve initial value problems. It requires fewer function evaluations than the traditional Runge-Kutta methods making it computationally more efficient in achieving the required accuracy. The author will utilize the combination of the GLM with initial value methods to solve the linear fuzzy BVP's and a shooting-like method for the nonlinear cases. Numerical testing and simulation of several examples, considered by other authors, will be presented to show the efficiency of the proposed method.

Fuzzy Volterra Integro-Differential Equations Using General Linear Method

In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalues of a multisteps method. The derivation of general linear method is based on the theory of B-series and rooted trees. Here, the fuzzy general linear method using the approach of generalized Hukuhara differentiability and combination of composite Simpson’s rules together with Lagrange interpolation polynomial is constructed for numerical solution of fuzzy volterra integro-differential equations. To illustrate the performance of the method, the numerical results are compared with some existing numerical methods.

Timing of Lower Extremity Motions during Barefoot and Shod Running at Three Velocities

This study investigates the timing differences between subtalar and knee joint movement of 9 male subjects while running barefoot and shod at three velocities. An alternative approach is used by dividing the pronation curve into 3 phases. Consequently, the timing of the maximum pronation phase was evaluated, not just the event of the maximum pronation value. Statistical differences were tested using the General Linear Method and paired t tests (p £.05), The extension of the knee starts both barefoot and shod significantly earlier than the resupination phase. Individual analysis shows that a larger time discrepancy between knee extension and the end of pronation mainly depends on the presence of bimodal pronation curves. The relative time differences significantly diminish with increased running velocity. Results suggest that by using this alternative approach, more detailed and useful information is available to describe the lime relationship between flexion-extension of the knee and pro-supination.