In a recent study, we investigate the Burgers–Fisher equation through developed scheme, namely, non-polynomial spline fractional continuity method. The proposed models represent nonlinear optics, chemical physics, gas dynamics, and heat conduction. basic concept of new approach is constructing with instead natural derivative. Furthermore, truncation error analyzed to determine order convergence...

The famous de Boor conjecture states that the condition of the polynomial B-spline collocation matrix at the knot averages is bounded independently of the knot sequence, i.e., it depends only on the spline degree. For highly nonuniform knot meshes, like geometric meshes, the conjecture is known to be false. As an effort towards finding an answer for uniform meshes, we investigate the spectral c...

In this paper, we discuss the problem of instability in the dimension of a spline space over a T-mesh. For bivariate spline spaces S (5, 5, 3, 3) and S (4, 4, 2, 2), the instability in the dimension is shown over certain types of T-meshes. This result could be considered as an attempt to answer the question of how large the polynomial degree (m,m) should be relative to the smoothness (r, r) to ...

Let 2 be a polyhedral complex embedded in the euclidean space Ed and Sr(2), r ≥ 0, denote the set of all Cr-splines on 2. Then Sr(2) is an R-module where R = E[x1, . . . , xd] is the ring of polynomials in several variables. In this paper we state and prove the existence of an algorithm to write down a free basis for the above R-module in terms of obvious linear forms defining common faces of m...

Abstract Bézier splines are widely available in various systems with the curves and surface designs. In general, the Bézier spline can be specified with the Bézier curve segments and a Bézier curve segment can be fitted to any number of control points. The number of control points determines the degree of the Bézier polynomial. This paper presents a method which determines control points for Bé...

The major problem when building shape models by minimising the description length (DL) is the computationally demanding optimisation in a highdimensional space. To speed up the convergence when dealing with discretised contours, Ericsson and Åström [6] have shown how to approximate and how to exploit the gradient of the DL. We derive the gradient of the DL for differentiable training sets. Addi...

For a function f 2 L p ?1; 1], 0 < p < 1, with nitely many sign changes, we construct a sequence of polynomials P n 2 n which are copositive with f and such that kf ? P n k p C! ' (f; (n + 1) ?1) p , where ! ' (f; t) p denotes the Ditzian-Totik modulus of continuity in L p metric. It was shown by S. P. Zhou that this estimate is exact in the sense that if f has at least one sign change, then ! ...