Mathematical tidal model of the Tay Estuary

1980 ◽  
Vol 78 (3-4) ◽  
pp. s171-s182
Author(s):  
D. J. A. Williams ◽  
V. Nassehi
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Tidal Range ◽  
Level Curve ◽  
Tidal Level ◽  
Tidal Model ◽  
One Dimensional ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Tay Estuary

SynopsisA one-dimensional mathematical model based on an implicit finite difference scheme is used to predict tidal levels and discharges throughout the Tay Estuary. The model accounts for the transformation of the tidal level curve along the estuary and predicts a maximum tidal range near Flisk. There is a measure of agreement between computed velocities and observed data in the upper reaches of the estuary.

scholarly journals One-dimensional model for the computation of unsteady salinity intrusion in a river

1982 ◽  
Vol 4 (3) ◽  
pp. 1-15
Author(s):  
Nguyen Van Diep ◽  
Nguyen Tat Dac ◽  
Tran Ngoc Duyet
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Numerical Technique ◽  
Momentum Equation ◽  
Transient Condition ◽  
Salinity Intrusion ◽  
Dimensional Model ◽  
One Dimensional ◽  
Tidal Motion ◽  
Implicit Finite Difference

The study is concerned with the development of a predictive, on – dimensional. Mathematical model for the salinity intrusion in a river. This is accomplished by means of simultaneous weighted implicit finite difference solutions to the salt balance equation and to the continuity and momentum equation which definite the tidal motion. It is shown that the boundary condition on salinity at downstream can be specified by using one condition during the flood tide and another condition during the ebb-tide. The resulting mathematical model, as solved by a finite-difference numerical technique can be used in a predictive manner for transient condition of downstream, surface elevation and time-varying fresh water discharges at upstream.

scholarly journals One-dimensional finite difference schemes for splitting method realization in axisymmetric equations of the dynamics of elastic medium

2021 ◽  
pp. 47-66
Author(s):  
В.М. Садовский ◽  
О.В. Садовская ◽  
Е.А. Ефимов
Keyword(s):  
Energy Dissipation ◽  
Finite Difference ◽  
Splitting Method ◽  
Finite Difference Schemes ◽  
Computing Systems ◽  
One Dimensional ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Comparison Of The Results ◽  
Predictor Corrector

Строятся экономичные разностные схемы сквозного счета для решения прямых задач сейсмики в осесимметричной постановке. При распараллеливании алгоритмов, реализующих схемы на многопроцессорных вычислительных системах, применяется метод двуциклического расщепления по пространственным переменным. Одномерные системы уравнений на этапах расщепления решаются на основе явных сеточно-характеристических схем и неявной разностной схемы типа "предиктор-корректор" с контролируемой искусственной диссипацией энергии. Верификация алгоритмов и программ выполнена на точных решениях одномерных задач типа бегущих монохроматических волн. Сравнение результатов показало неоспоримые преимущества схемы с контролируемой диссипацией энергии по точности расчета гладких решений и целесообразность применения явных монотонных схем при расчете разрывов. We construct efficient finite difference shock-capturing schemes for the solution of direct seismic problems in axisymmetric formulation. When parallelizing the algorithms implementing the schemes on multiprocessor computing systems, the two-cyclic splitting method with respect to the spatial variables is used. One-dimensional systems of equations are solved at the stages of splitting on the basis of explicit gridcharacteristic schemes and an implicit finite difference scheme of the “predictor–corrector” type with controllable artificial energy dissipation. The verification of algorithms and programs is fulfilled on the exact solutions of one-dimensional problems describing traveling monochromatic waves. The comparison of the results showed the advantages of the scheme with controllable energy dissipation in terms of the accuracy of computing smooth solutions and the advisability of application of explicit monotone schemes when calculating discontinuities.

scholarly journals A robust numerical solution to a time-fractional Black–Scholes equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. M. Nuugulu ◽  
F. Gideon ◽  
K. C. Patidar
Keyword(s):  
Finite Difference ◽  
Stock Options ◽  
Stochastic Dynamics ◽  
European Options ◽  
Numerical Convergence ◽  
Put Option ◽  
Implicit Finite Difference Scheme ◽  
Black Scholes ◽  
Implicit Finite Difference ◽  
Rigorous Mathematical Analysis

AbstractDividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work are appropriate for capturing market fluctuations in which random fractional white noise has the potential to accurately estimate European put option premiums while providing a good numerical convergence. The aim of this paper is two fold: firstly, to construct a time-fractional (tfBS) PDE for pricing European options on continuous dividend paying stocks, and, secondly, to propose an implicit finite difference method for solving the constructed tfBS PDE. Through rigorous mathematical analysis it is established that the implicit finite difference scheme is unconditionally stable. To support these theoretical observations, two numerical examples are presented under the proposed fractional framework. Results indicate that the tfBS and its proposed numerical method are very effective mathematical tools for pricing European options.

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