In this paper, we construct a numerical ‎method‎ to ‎the ‎solution ‎of‎ the Black-Scholes partial differential equation modeling the European option pricing problem with regard to a single asset‎. ‎W‎e use an explicit spline-difference scheme which is based on using a finite difference approximation for the temporal derivative and a cubic B-spline collocation for spatial derivatives. ‎The deriv...

Abstract To obtain higher order continuous tool path, a cubic B-spline curve fitting method is presented in this paper to process the linear path. First, local polynomial with bidirectional scanning scheme proposed determine some initial dominant points. Based on these points, knot vector generated by average method, and constructed. constrain error, Newton’s based error estimation point insert...

A numerical scheme, based on the cubic B-spline wavelets for solving fractional integro-differential equations is presented. The fractional derivative of these wavelets are utilized to reduce the fractional integro-differential equation to system of algebraic equations. Numerical examples are provided to demonstrate the accuracy and efficiency and simplicity of the method.

In this paper, a class of singular two-point boundary value problems are solved using hybrid cubic B-spline method. algorithm, free parameter γ plays an important role to give accurate converge results for the solution. This chosen via optimization. Numerical examples displayed prove that our suggested method is flexible and effective, numerical compared with other methods from literature

In this paper we present a new method for the model of interpolation sweep surfaces by the C-continuous generalized quasicubic interpolation spline. Once given some key position, orientation and some points which are passed through by the spine and initial cross-section curves, the corresponding sweep surface can be constructed by the introduced spline function without calculating control point...

introduction relative dose computation is a necessary step in radiation treatment planning. therefore, finding an approach that is both fast and accurate seems to be necessary. the purpose of this work was to investigate the feasibility of natural cubic spline to reconstruct dose maps for linear accelerator radiation treatment fields in comparison with those of the simulation. materials and met...

This paper presents a method for planning the motions of autonomous vehicles moving on general terrains. The method obtains the geometric path and vehicle speeds that minimize motion time considering vehicle dynamics, terrain topography, obstacles, and surface mobility. The terrain is represented by a smooth cubic B patch, and the geometric path consists of a B spline curve mapped to the surfac...