Fully Coupled Numerical Methods for Elastohydrodynamic Lubrication Line Contact Problems by the High Order Finite Difference Methods

In this paper a high order finite difference method is constructed to solve the elastohydrodynamic lubrication line contact problems, whose cavitation condition is handled by the penalty method. The highly nonlinear equations from the discretization of the high order finite difference method are solved by the trust-region dogleg algorithm. In order to reduce the numerical dissipation and dispersion brought by the high order upwind finite difference scheme, a high order biased upwind finite difference scheme is also presented. Our method is found to achieve more accurate solutions using just a small number of nodes compared to the multilevel methods combined with the lower order finite difference method.

Physics-Capturing Discretizations for Spectral Wind-Wave Models

This paper discusses the discretization methods that have been commonly employed to solve the wave action balance equation, and that have gained a renewed interest with the widespread use of unstructured grids for third-generation spectral wind-wave models. These methods are the first-order upwind finite difference and first-order vertex-centered upwind finite volume schemes for the transport of wave action in geographical space. The discussion addresses the derivation of these schemes from a different perspective. A mathematical framework for mimetic discretizations based on discrete calculus is utilized herein. A key feature of this algebraic approach is that the process of exact discretization is segregated from the process of interpolation, the latter typically involved in constitutive relations. This can help gain insight into the performance characteristics of the discretization method. On this basis, we conclude that the upwind finite difference scheme captures the wave action flux conservation exactly, which is a plus for wave shoaling. In addition, we provide a justification for the intrinsic low accuracy of the vertex-centred upwind finite volume scheme, due to the physically inaccurate but common flux constitutive relation, and we propose an improvement to overcome this drawback. Finally, by way of a comparative demonstration, a few test cases is introduced to establish the ability of the considered methods to capture the relevant physics on unstructured triangular meshes.

Metode Numerik Untuk Menentukan Harga Opsi Dengan Model Volatilitas Leland

Option price under transaction cost with leland volatility model is the solution of a non linear diferential equations. To solve this equation used numerical methods based on an upwind finite difference for spatial discretization as well as the use of explicit and implicit methods for discretizing time-stepping. upwind finite difference method with explicit time-stepping scheme proved to be unstable so as not konvegen. While the use of implicit time-stepping scheme is proved monotonous, consistent and stable so that converge to the viscosity solution.