In this paper a rational cubic algebraic spline with two shape parameters is developed to create a high-order smoothness interpolation using function values and derivative values which are being interpolated. This is a kind of rational cubic interpolation with quadratic denominator. This rational spline interpolant is monotonic interpolant to given monotonic data. The more important achievement...

In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k + kh + h) for the solution of quasi-linear parabolic equation   , , , , xx x t u f x t u u u  , 0< x <1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline app...

Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniform partitions, and an optimal collocation method are derived for solving Bratu-type equations. Numerical examples are presented to verify the efficiency and accuracy of these methods when compared to other nume...

We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R+ such that the reconstruction wavelets are divergence-free and have vanishing normal components on the boundary of R+. Such wavelets are suitable to study the Navier–Stokes equation...

This paper gives a construction to complete, at extraordinary points, an otherwise bi-cubic spline surface – so that the resulting surface is curvature continuous everywhere. To fill the n-sided gap in the bi-cubic surface, a cap is constructed from n spline patches, each consisting of 2× 2 pieces of polynomial degree bi-5. Particular care is taken to continue the curvature distribution from th...

In the work of solving a uniformly elliptic differential equations Au := − u+ a1ux + a2uy + a0u = f in the unit square with boundary conditions by the C1-cubic spline collocation method, one may need to investigate efficient preconditioning techniques. For this purpose, using the generalized field of values argument, we show the uniform bounds of the eigenvalues of the preconditioned matrix whe...

Gradient information is used in volume rendering to classify and color samples along a ray. In this paper we present an analysis of the theoretically ideal gradient estimator and compare it to some commonly used gradient estimators. A new method is presented to calculate the gradient at arbitrary sample positions, using the derivative of the interpolation lter as the basis for the new gradient ...

In this paper, we present a real-time algorithm that plans mostly optimal trajectories for multiple mobile robots in a dynamic environment. This approach combines the use of a Delaunay triangulation to discretise the environment, a novel efficient use of the A* search method, and a novel cubic spline representation for a robot trajectory that meets the kinematic and dynamic constraints of the r...

We consider the problem of variational interpolation of subsets of Euclidean spaces by curves such that the L norm of the second derivative is minimized. It is well known that the resulting curves are cubic spline curves. We study geometric boundary conditions arising for various types of subsets such as subspaces, polyhedra, and submanifolds, and we indicate how solutions can be computed in th...

In the modeling of continuous time systems, there is a need to convert the analog system to a discrete time system. The transform frequently encountered in the literature is the impulse invariant transform. This transform has proven to be inadequate for biological system modeling. In this paper we will review the available linear transforms and derive three new transforms, namely the centered s...