In this paper, Numerical Methods for solving ordinary differential equations, beginning with basic techniques of finite difference methods for linear boundary value problem is investigated. Numerical solution is found for the boundary value problem using finite difference method and the results are compared with analytical solution. MATLAB coding is developed for the finite difference method. T...

Dense phase pneumatic conveying has been investigated through simulation, using a discrete element approach for the granular particles and a finite difference method for the pressure field. Both horizontal and vertical conveying are studied and compared. Studies of single plugs or slugs promise to give insight into the performance of pneumatic conveying systems.

In this paper, we present a numerical approach to a class of nonlinear reactiondiffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. ...

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems.

The goal of this work is to determine classes of traveling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz.

We develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the L2 norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite d...

We characterize orthogonal matrix polynomials (Pn)n whose differences (∇ Pn+1)n are also orthogonal by means of a discrete Pearson equation for the weight matrix W with respect to which the polynomials (Pn)n are orthogonal. We also construct some illustrative examples. In particular, we show that contrary to what happens in the scalar case, in the matrix orthogonality the discrete Pearson equat...

This paper describes a technique for timestamping data from an array of sensors. This is a challenging issue that needs to be solved for the magnetometry-based navigation system presented here. This system uses finite difference schemes to evaluate spatial and time derivatives of a vector field. The accuracy of the timestamping method is critical. In the context of this particular application, ...

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We study a superreplication problem of European options with gamma constraints, in mathematical finance. The initially unbounded control problem is set back to a problem involving a viscosity PDE solution with a set of bounded controls. Then a numerical approach is introduced, inconditionnally stable with respect to the mesh steps. A generalized finite difference scheme is used since basic fini...