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...

An analysis of single-electron orbits in combined coaxial wiggler and axial guide magnetic fields is presented. Solutions of the equations of motion are developed in a form convenient for computing orbital velocity components and trajectories in the radially dependent wiggler. Simple analytical solutions are obtained in the radially-uniform-wiggler approximation and a formula for the derivative...

The construction of solution-adapted meshes is addressed within an optimization framework. An approximation of the second spatial derivative of the solution is used to get a suitable metric in the computational domain. A mesh quality is proposed and optimized under this metric, accounting for both the shape and the size of the elements. For this purpose, a topological and geometrical mesh impro...

We look for the approximation of exp(A1 + A2) by a product in form exp(x1A1) exp(y1A2) · · · exp(xnA1) exp(ynA2). We specially are interested in minimal approximations, with respect to the number of terms. After having shown some isomorphisms between specific free Lie subalgebras, we will prove the equivalence of the search of such approximations and approximations of exp(A1 + · · ·+ An). The m...

In this paper, we consider fractional differential equations with the new derivative involving a nonsingular kernel, namely, Caputo-Fabrizio derivative. Using successive approximation method, prove an extension of Picard-Lindelöf existence and uniqueness theorem for derivative, which gives set conditions, under initial value problem has unique solution.

An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation the Legendre orthogonal polynomials, while time derivative discretized by using symmetric Euler finite difference schema. stability convergence of ...

In this paper, a high-order and unconditionally stable difference method is proposed for the numerical solution of onespace dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivative of this equation and a Padé approximation of fifth-order for the resulting system of ordinary differential equations. It is shown ...

Many time-domain problems in engineering applications can be described by means of a parameter dependent time-invariant dynamic systems. We are interested in parameter estimation, by fitting available transient measurements using the nonlinear least square method. As the main application, we consider the control source electromagnetic method (CSEM) of geophysical exploration governed by the dif...

For weighted approximation in Lp-norm, we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the r-fold integrated Wiener space. AMS subject classifications: 41A28, 65D05, 41A25