In the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten, this paper presents an extension of a previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold....

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the...

American options are priced numerically using a space- and time-adaptive finite difference method. The generalized Black–Scholes operator is discretized on a Cartesian structured but non-equidistant grid in space. The space- and time-discretizations are adjusted such that a predefined...

We construct a class of symplectic integration schemes to general Sine–Gordon type systems. We also conduct several numerical tests for these symplectic schemes. Our numerical results demonstrate the effectiveness of these schemes for numerical computation of the solutions to the general...

In this paper, we consider the solution of the modified Burger's equation by using the collocation method with quintic splines. Applying the Von-Neumann stability analysis method we show that the proposed method is unconditionally stable. By conducting a comparison between the absolute error for...

Numerical procedures for the solution of an inverse problem of determining unknown source parameter in a parabolic equation are considered. Two different numerical procedures are studied and their comparison analysis is presented. One of these procedures obtained by introducing transformation of...

In this paper we present a formulation of a finite difference Crank–Nicolson scheme for the numerical solution of the unsteady heat equation in 2+1 dimensions, a problem which has not been extensively studied when the spatial domain has an irregular shape. It is based on a second order...

The coupled nonlinear Schrödinger equation models several intersting physical phenomena. It presents a model equation for optical fiber with linear birefringence. In this paper, we present a linearly implicit conservative method to solve this equation. This method is second order accurate in...