In this work, a space-time multigrid method which uses standard coarsening in both temporal and spatial domains and combines the use of different smoothers is proposed for the solution of the heat equation in one and two space dimensions. In particular, an adaptive smoothing strategy, based on the degree of anisotropy of the discrete operator on each grid-level, is the basis of the proposed mul...

Abstract. We study the error estimates for the alternating evolution discontinuous Galerkin (AEDG) method to one dimensional linear convection-diÆusion equations. The AEDG method for general convection-diÆusion equations was introduced in [H. Liu, M. Pollack, J. Comp. Phys. 307: 574–592, 2016], where stability of the semi-discrete scheme was rigorously proved for linear problems under a CFL-lik...

In this study, a new algorithm is introduced for the numerical solution of equal width (EW) equation. This created by using collocation finite element method based on decic B-spline functions space discretization EW equation and Crank-Nicolson time his The obtained results are compared with previous ones to see efficiency accuracy proposed method.

We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann–Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank...

In this paper, we construct a new numerical algorithm for the partial differential equation of up-and-out put barrier options under CEV model. method, use Crank-Nicolson scheme to discrete temporal variables and cubic B-spline collocation method spatial variables. The is stable has second-order convergence both time space analysis proposed discussed in detail. Finally, examples verify stability...

Differentiation matrices provide a compact and unified formulation for a variety of differential equation discretisation and timestepping algorithms. This paper illustrates their use for solving three differential equations of finance: the classic Black-Scholes equation (linear initial-boundary value problem), an American option pricing problem (linear complementarity problem), and an optimal m...

In this paper we present a PDE formulation for the ratchet cap pricing problem. The underlying LIBOR interest rates are assumed to follow the LIBOR market model. For this PDE problem the existence and uniqueness of solution are obtained in the classical framework of uniformly parabolic PDEs in terms of a sequence of nested Cauchy problems. Moreover, this approach allows to obtain a new numerica...