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...

This paper discusses the application of orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions partial differential equations. Collocation is performed at Gaussian points to obtain an optimal solution, hence name collocation. The used solve various cases Burgers’ equations, including modified equation. KdV–Burgers’ equation considered as a tes...

Among fitted-operator methods for solving one-dimensional singular perturbation problems one of the most accurate is the collocation by linear combinations of {1, x, exp (±px)}, known as tension spline collocation. There exist well established results for determining the ‘tension parameter’ p, as well as special collocation points, that provide higher order local and global convergence rates. H...