In financial markets, dynamics of underlying assets are often specified via stochastic differential equations of jump-diffusion type. In this paper, we suppose that two financial assets evolved by correlated Brownian motion. The value of a contingent claim written on two underlying assets under jump diffusion model is given by two-dimensional parabolic partial integro-differential equation ( P I D E ), which is an extension of the Black-Scholes equation with a new integral term. We show how basket option prices in the jump-diffusion models, mainly on the Merton model, can be approximated using Finite Difference Method. To avoid a dense linear system solution, we compute the integral term by using the Trapezoidal Method. The numerical results show the efficiency of proposed Method.

In this paper, a moving mesh technique and a non-standard Finite Difference Method are combined, and amoving mesh non-standard Finite Difference (MMNSFD) Method is developed to solve an initial boundary valueproblem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this Method, the movingspatial grid is obtained by a simple geometric adaptive algorithm to preserve stability. Moreover, it uses variable timesteps to protect the positivity condition of the solution. The results of this computational technique are comparedwith the corresponding uniform mesh non-standard Finite Difference scheme. The simulations show that the presentedMethod is efficient and applicable, and approximates the solutions well, while because of producing unreal solution, the corresponding uniform mesh non-standard Finite Difference fails.

In this study, we solve the Fokker-Planck equation by a compact Finite Difference Method, By the Finite Difference Method the computation of Fokker-Planck equation is reduced to a system of ordinary differential equations. Two different Methods, boundary value Method and cubic C1-spline collocation Method, for solving the resulting system are proposed. Both Methods have fourth-order accuracy in time variable. By the boundary value Method, some pointwise approximate solutions are only obtained. But, C1-spline Method gives a closed-form approximation in each space step, too. Illustrative examples are included to demonstrate the validity and efficiency of the Methods. A comparison is made with existing results.