generalized solution on neumann problem of the fourth order ordinary dierential equation in space w2 (0; b) has been discussed , we obtain the condition on b.v.p when the solution is in classical form. formulation of quintic spline function has been derived and the consistency relations are given.numerical method,based on quintic spline approximation has been developed. spline solution of the...

‎In this paper we introduce a numerical approach that solves optimal control problems (OCPs) ‎using collocation methods‎. ‎This approach is based upon B-spline functions‎. ‎The derivative matrices between any two families of B-spline functions are utilized to‎ ‎reduce the solution of OCPs to the solution of nonlinear optimization problems‎. ‎Numerical experiments confirm our heoretical findings‎.

For a given triangulation 4 of a region R of interest, let S 2 8 (4) := fs 2 C 2 (R) : sj t 2 IP 8 ; 8t 2 4g be the space of all splines of degree 8 and smoothness 2, where t denotes any triangle of 4 and IP 8 the space of polynomials of total degree 8. Furthermore, let b S 2 8 (4) := fs 2 S 2 8 (4) : s 2 C 3 at v;8v 2 4g be a super spline subspace of S 2 8 (4). We construct a collection of loc...

Unlike the visual trimming of B-spline surfaces, which hides unwanted portions in rendering, the geometric trimming approach provides a mathematically clean representation without redundancy. However, the process may lead to significant deviation from the corresponding portion on the original surface. Optimization is required to minimize approximation errors and obtain higher accuracy. In this ...

In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is ...

We consider the self-adjoint singularly perturbed two-point boundary value problems. We know that the numerical methods for solution of such problems based on nonpolynomial spline in grid points, can produce the fourth order method only. So that we look for an alternative to obtain higher order methods. We develop the non-polynomial spline in off-step points to rise the order of accuracy. Based...

The estimation of functions with varying degrees smoothness is a challenging problem in the nonparametric function estimation. In this paper, we propose LABS (L\'{e}vy Adaptive B-Spline regression) model, an extension LARK models, for smoothness. model B-spline bases as generating kernels. basis consists piecewise k degree polynomials k-1 continuous derivatives and can express systematically By...

The fast solution of linear systems arising from an isogeometric discretization of a partial differential equation is of great importance for the practical use of Isogeometric Analysis. For classical finite element discretizations, multigrid methods are well known to be fast solvers showing optimal convergence behavior. However, if a geometric multigrid solver is naively applied to a linear sys...

The matrix forms for curves and surfaces were largely promoted in CAD/CAM. In this paper we have presented two matrix representation formulations for arbitrary degree NURBS curves and surfaces explicitly other than recursively. The two approaches are derived from the computation of divided difference and the Marsden identity respectively. The explicit coefficient matrix of B-spline with equally...

We present a system for fast and accurate display of CSG constructive solid geome try models Such models have as primitives polyhedra and solids whose boundaries can be represented using rational spline surfaces As part of pre processing we compute the B rep boundary representation from the CSG tree and represent the resulting solid using trimmed spline surfaces No assumptions are made on the n...