The interpolation method in a semi-Lagrangian scheme is decisive to its performance. Given the number of grid points one is considering to use for the interpolation, it does not necessarily follow that maximum formal accuracy should give the best results. For the advection equation, the driving force of this method is the method of the characteristics, which accounts for the flow of information in the model equation. This leads naturally to an interpolation problem since the foot point is not in general located on a grid point. We use another interpolation scheme that will allow achieving the high order for the box initial condition.
This paper describes a numerical solution for a two-point boundary value problem. It includes an algorithm for discretization by mixed finite element method. The discrete scheme allows the utilization a finite element method based on piecewise linear approximating functions and we also use the barycentric quadrature rule to compute the stiffness matrix and the L2-norm.
In this work the Adomian decomposition method (ADM) is used to solve the non-linear equation that represents the generalized model of Black-Scholes, that is to say that considers the volatility as a nonconstant function. The efficiency of this method is illustrated by investigating the convergence results for this type of models. The numerical results show the reliability and accuracy of the ADM.
We establish the conditions for the compute of the Global Truncation Error (GTE), stability restriction on the time step and we prove the consistency using forward Euler in time and a fourth order discretization in space for Heat Equation with smooth initial conditions and Dirichlet boundary conditions.
This article presents an analysis of the chaotic dynamics presented by the Lorenz system and how this behavior can be eliminated through the implementation of sliding mode control. It is necessary to know about the theory of stability of Lyapunov to develop the appropriate control that allows to bring the system to the desired point of operation.
The purpose of this paper is to present the capabilities of the conjugate gradient methods based on the theoretical analysis of the gradient method, the precursor of the descent methods. It indicates the geometric differences of these and the improvements made in the search for the optimal value of an objective function. Different test systems are proposed to solve, in order to obtain a solution that can determine the speed of convergence of the conjugate address proposed by Liu-Storey and Dai-Yuan [1].
The chaos in a system is a very important element for a complete analysis in its dynamics. This is an indicator that allows to quantify this phenomenon which can be studied using the exponents of Lyapunov [1]. Here we present the methodology of determining them from the dynamics of the system (differential equations). When the dynamics of the system are known, it is necessary to reconstruct the phase space from the time series that are arranged.
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