In this study, trigonometric quintic B-spline collocation method is constructed for computing numerical solutions of the reaction-diffusion system (RDS). Schnakenberg, Gray-Scott and Brusselator models are special cases systems considered as examples in paper. Crank-Nicolson formulae used time discretization generalized RDS nonlinear terms time-discretized form linearized using Taylor expansion...

The interpolation of a planar sequence of points p0, . . . , pN by shape-preserving G 1 or G2 PH quintic splines with specified end conditions is considered. The shape-preservation property is secured by adjusting ‘tension’ parameters that arise upon relaxing parametric continuity to geometric continuity. In the G2 case, the PH spline construction is based on applying Newton–Raphson iterations ...

This paper explains about a neural network based control scheme to determine trajectory control parameters i.e. velocity, acceleration and jerk for a industrial robot performing a defined task. The proposed approach is the blend of quintic B-spline and neural network system for prediction of joint control parameters. The proposed approach is applied to a case of three robot trajectory control p...

Functional biologists employ numerical differentiation for many purposes, including (1) estimation of maximum velocities and accelerations as measures of behavioral performance, (2) estimation of velocity and acceleration histories for biomechanical modeling, and (3) estimation of curvature, either of a structure during movement or of the path of movement itself. I used a computer simulation ex...

A piecewise quintic G spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular B ezier representation, is a ne invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G continuously around a common vertex is solved by constructi...

In this paper, the collocation method is performed with quintic B-spline functions on a uniform mesh to obtain the numerical solutions of Fisher’s equation. Crank-Nicolson method is used for time discretization. Von Neumann stability analysis shows that the given method is conditionally stable. In order to observe the effects of reaction and diffusion, four test problems related to pulse distur...

The interpolation of discrete spatial data — a sequence of points and unit tangents — by G1 Pythagorean– hodograph (PH) quintic spline curves, under shape constraints, is addressed. To achieve this, a local Hermite scheme incorporating a tension parameter for each spline segment is employed, the imposed shape constraints being concerned with preservation of convexity at the knots and the sign o...