The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effecti...

We establish rigorously the fundamental nesting behavior of T-spline spaces in terms of the topology of the T-mesh. This provides a theoretical foundation for local refinement algorithms based on analysis-suitable T-splines and their use in isogeometric analysis. A key result is a dimension formula for smooth polynomial spline spaces defined over the Bézier mesh of a T-spline.

Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

Abstract. We describe and demonstrate an arrow notation for deriving box-spline subdivision schemes. We compare it with the z-transform, matrix, and mask convolution methods of deriving the same. We show how the arrow method provides a useful graphical alternative to the three numerical methods. We demonstrate the properties that can be derived easily using the arrow method: mask, stencils, con...

The paper presents the differential quadrature method (DQM) based on a modified spline interpolation and the application of the method in vibration analysis of laminated, composite shells. The goal of the modification of the spline interpolation is to improve the rate of convergence and preserve the stability of the method. The modification changes the definition of the end conditions for the s...

It is proved that, among all nonnegative bases of its space, the B-spline basis is optimally stable for evaluating spline functions.

This paper shows that, for any given T-spline, the linear independence of its blending functions can be determined by computing the nullity of the T-spline-to-NURBS transform matrix. The paper analyzes the class of Tsplines for which no perpendicular T-node extensions intersect, and shows that the blending functions for any such T-spline are linearly independent.

Analogous to the quadratic B-spline curve, a piecewise quadratic trigonometric polynomial curve is presented in this paper. The quadratic trigonometric polynomial curve has C2 continuity, while the quadratic B-spline curve has C1 continuity. The quadratic trigonometric polynomial curve is closer to the given control polygon than the quadratic B-spline curve.

The non-polynomial spline method is proposed to solve a singular boundary value problems. Some model problems are solved and the numerical results are compared with B-spline approximation and the exact solution. Results obtained by the method indicate the method is simple and effective. Key–Words: Singular point; Singular two-point boundary value problems; Cubic spline