Many mathematical formulations of physical phenomena contain integro-differential equations. In this paper a numerical method is developed to solve the convection-diffusion integro-differential equations with a weakly singular kernel using the cubic B-spline collocation method. These equations occur in many applications such as in the transport of air and ground water pollutants, oil reservoir ...

In this work, we present a generalized method for analysis of data series based on shape constraint spline fitting which constitutes the first step towards a statistically optimal method for qualitative analysis of trends. The presented method is based on a branch-and-bound (B&B) algorithm which is applied for globally optimal fitting of a spline function subject to shape constraints. More spec...

In this paper, we develop a new cubic spline method for computing approximate solution of a system of fourth-order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and gives approximations which are better than those produced by some other collocation, finite difference and spline methods. Numerical examples a...

A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization technique to reduce the nonlinear problems to linear problems and use B-spline collocation method, which leads to a seven nonzero bands linear system. Illustrative example is included ...

Abstract A real-time path generation method with Non Uniform Rational B Spline(NURBS) technology in the Computer Aided Design(CAD) field is presented and realized in a five-axis Computer Numerically Controlled(CNC) system. In this method, the tool path was represented into two NURBS curves, tooltip and tool-orientation spline curve, based on the same knot vector. The Cutter Location(CL) data wa...

A quadratic non-polynomial spline functions based method is developed to find approximations solution to a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The present approach has less computational cost and gives better approximations than those produced by other collocation, finite-difference and spline methods. Convergence analysis o...

A collocation method based on modified cubic B-spline functions has been developed for the valuation of European, American and barrier options of a single asset. The new approach contains discretization of temporal derivative using finite difference approximation of and approximating the option price with the modified B-spline functions. Stability of this method has been discussed and it is sho...

A B-spline collocation method is developed for solving boundary value problems which arise from the problems of calculus of variations. Some properties of the B-spline procedure required for subsequent development are given, and they are utilized to reduce the solution computation of boundary value problems to some algebraic equations. The method is applied to a few test examples to illustrate ...

Use of mathematical interpolation in Digital Signal Processing applications often seems to be a remarkable solution when applied for noise reduction. In the last two decades advancement in the Elasticity imaging of tissue is worth mentioning. Two dimensional spline technique for generating Elastograms is fairly a new approach for generating ultrasonic Elastograms. In the way of analyzing imagin...

This paper presents a fully Bayesian approach to regression splines with automatic knot selection in generalized semiparametric models for fundamentally non Gaussian responses In a basis function representation of the regression spline we use a B spline basis The reversible jump Markov chain Monte Carlo method allows for simultaneous estimation both of the number of knots and the knot placement...