scholarly journals An Efficient Method for Solving Spread Option Pricing Problem: Numerical Analysis and Computing

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
R. Company ◽  
V. N. Egorova ◽  
L. Jódar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Analysis ◽  
Option Pricing ◽  
Computational Time ◽  
Explicit Difference Scheme ◽  
Spatial Variables ◽  
One Dimensional ◽  
Spread Option ◽  
The One

This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. Taking advantage of a cross derivative removing technique, an explicit difference scheme is developed retaining the benefits of the one-dimensional finite difference method, preserving positivity, accuracy, and computational time efficiency. Numerical results illustrate the interest of the approach.

Numerical analysis of the convection and diffusion of solutes to roots

Soil Research ◽  
1967 ◽  
Vol 5 (2) ◽  
pp. 149 ◽  
Author(s):  
JB Passioura ◽  
MH Frere
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Medium ◽  
Diffusion Coefficient ◽  
Numerical Analysis ◽  
Average Concentration ◽  
Soil System ◽  
Dry Soil ◽  
The One ◽  
And Diffusion

A numerical method is given for solving a partial differential equation describing the radial movement of solutes through a porous medium to a root. Computer programmes based on the method were prepared and used to obtain solutions of the equation for an idealized root-soil system in which a solute is transported to the root by convection but is not taken up by the root. Various patterns of water uptake were considered, the most complex being a diurnally varying uptake from soil in which the water content is decreasing. The solutions suggest that the maximum build-up of solute at the surface of a root is trivial if the root is growing in a medium such as agar, in which the diffusion coefficient of the solute is high, but may be considerable, with a concentration up to 10 times higher than the average concentration in the soil solution, when the root is growing in a fairly dry soil. The application of the method to systems other than the one considered in detail is discussed.

scholarly journals On the numerical solution of the one-dimensional convection-diffusion equation

2005 ◽  
Vol 2005 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Partial Differential ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The One

The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes several finite difference schemes for solving the one-dimensional convection-diffusion equation with constant coefficients. In this research the use of modified equivalent partial differential equation (MEPDE) as a means of estimating the order of accuracy of a given finite difference technique is emphasized. This approach can unify the deduction of arbitrary techniques for the numerical solution of convection-diffusion equation. It is also used to develop new methods of high accuracy. This approach allows simple comparison of the errors associated with the partial differential equation. Various difference approximations are derived for the one-dimensional constant coefficient convection-diffusion equation. The results of a numerical experiment are provided, to verify the efficiency of the designed new algorithms. The paper ends with a concluding remark.

scholarly journals Extension of ADMMAlgorithmin Solving Optimal Control Model Governed by Partial Differential Equation

2021 ◽  
pp. 105-115
Author(s):  
Kazeem adebowale Dawodu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Control Model ◽  
Partial Differential ◽  
One Dimensional ◽  
Alternating Direction ◽  
Primal Dual ◽  
Discrete Convex ◽  
The One

This paper presents an Algorithm for the numerical solution of the Optimal Control model constrained by Partial Differential Equation using the Alternating Direction Method of Multipliers (ADMM) accelerated with a parameter factor in the sense of Nesterov. The ADMM tool wasapplied to a partial differential equation-governed optimization problem of the one-dimensional heat equation type. The constraint and objective functions of the optimal control model were discretized using the Crank-Nicolson and Composite Simpson’s Methods respectively into a derived discrete convex optimization form amenable to the ADMM. The primal-dual residuals were derived to ascertain the rate of convergence of themodel for increasing iterates. An existing example was used to test the efficiency and degree of accuracy of the algorithm and the results were favorable when compared the existing method.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

scholarly journals Comparison of numerical schemes of river flood routing with an inertial approximation of the Saint Venant equations

RBRH ◽  
2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Alice César Fassoni-Andrade ◽  
Fernando Mainardi Fan ◽  
Walter Collischonn ◽  
Artur César Fassoni ◽  
Rodrigo Cauduro Dias de Paiva
Keyword(s):  
Numerical Stability ◽  
Flood Routing ◽  
Computational Time ◽  
Numerical Schemes ◽  
Time Step ◽  
Simple Formulation ◽  
One Dimensional ◽  
Saint Venant Equations ◽  
Original Scheme ◽  
The One

ABSTRACT The one-dimensional flow routing inertial model, formulated as an explicit solution, has advantages over other explicit models used in hydrological models that simplify the Saint-Venant equations. The main advantage is a simple formulation with good results. However, the inertial model is restricted to a small time step to avoid numerical instability. This paper proposes six numerical schemes that modify the one-dimensional inertial model in order to increase the numerical stability of the solution. The proposed numerical schemes were compared to the original scheme in four situations of river’s slope (normal, low, high and very high) and in two situations where the river is subject to downstream effects (dam backwater and tides). The results are discussed in terms of stability, peak flow, processing time, volume conservation error and RMSE (Root Mean Square Error). In general, the schemes showed improvement relative to each type of application. In particular, the numerical scheme here called Prog Q(k+1)xQ(k+1) stood out presenting advantages with greater numerical stability in relation to the original scheme. However, this scheme was not successful in the tide simulation situation. In addition, it was observed that the inclusion of the hydraulic radius calculation without simplification in the numerical schemes improved the results without increasing the computational time.

scholarly journals Simplified Grinding Temperature Model Study

2019 ◽  
Vol 6 (2) ◽  
pp. a1-a7
Author(s):  
N. V. Lishchenko ◽  
V. P. Larshin ◽  
H. Krachunov
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Heat Source ◽  
Boundary Conditions ◽  
Grinding Temperature ◽  
Temperature Model ◽  
One Dimensional ◽  
Heating And Cooling ◽  
Equation Of Heat Conduction ◽  
The One

A study of a simplified mathematical model for determining the grinding temperature is performed. According to the obtained results, the equations of this model differ slightly from the corresponding more exact solution of the one-dimensional differential equation of heat conduction under the boundary conditions of the second kind. The model under study is represented by a system of two equations that describe the grinding temperature at the heating and cooling stages without the use of forced cooling. The scope of the studied model corresponds to the modern technological operations of grinding on CNC machines for conditions where the numerical value of the Peclet number is more than 4. This, in turn, corresponds to the Jaeger criterion for the so-called fast-moving heat source, for which the operation parameter of the workpiece velocity may be equivalently (in temperature) replaced by the action time of the heat source. This makes it possible to use a simpler solution of the one-dimensional differential equation of heat conduction at the boundary conditions of the second kind (one-dimensional analytical model) instead of a similar solution of the two-dimensional one with a slight deviation of the grinding temperature calculation result. It is established that the proposed simplified mathematical expression for determining the grinding temperature differs from the more accurate one-dimensional analytical solution by no more than 11 % and 15 % at the stages of heating and cooling, respectively. Comparison of the data on the grinding temperature change according to the conventional and developed equations has shown that these equations are close and have two points of coincidence: on the surface and at the depth of approximately threefold decrease in temperature. It is also established that the nature of the ratio between the scales of change of the Peclet number 0.09 and 9 and the grinding temperature depth 1 and 10 is of 100 to 10. Additionally, another unusual mechanism is revealed for both compared equations: a higher temperature at the surface is accompanied by a lower temperature at the depth. Keywords: grinding temperature, heating stage, cooling stage, dimensionless temperature, temperature model.

scholarly journals On the Solvability of a Mixed Problem for a High-Order Partial Differential Equation with Fractional Derivatives with Respect to Time, with Laplace Operators with Spatial Variables and Nonlocal Boundary Conditions in Sobolev Classes

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 235 ◽  
Author(s):  
Onur İlhan ◽  
Shakirbay Kasimov ◽  
Shonazar Otaev ◽  
Haci Baskonus
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Mixed Problem ◽  
Fractional Derivatives ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Order Partial Differential Equation ◽  
Sobolev Classes ◽  
Spatial Variables

In this paper, we study the solvability of a mixed problem for a high-order partial differential equation with fractional derivatives with respect to time, and with Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes.

A limit theorem for certain disordered random systems

1994 ◽  
Vol 26 (04) ◽  
pp. 1022-1043 ◽  
Author(s):  
Xinhong Ding
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Limit Theorem ◽  
Random Systems ◽  
Joint Probability ◽  
Dynamical Behaviour ◽  
One Dimensional ◽  
Linear Stochastic Differential Equation ◽  
The One ◽  
Image Position

Many disordered random systems in applications can be described by N randomly coupled Ito stochastic differential equations in : where is a sequence of independent copies of the one-dimensional Brownian motion W and ( is a sequence of independent copies of the ℝ p -valued random vector ξ. We show that under suitable conditions on the functions b, σ, K and Φ the dynamical behaviour of this system in the N → (limit can be described by the non-linear stochastic differential equation where P(t, dx dy) is the joint probability law of ξ and X(t).

τ-D Decomposition to the One Dimensional Delay Differential Equation by Fixed the Coefficient b<0

2013 ◽  
Vol 785-786 ◽  
pp. 1418-1422
Author(s):  
Ai Gao
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Delay Differential Equation ◽  
Stability Domain ◽  
Transcendental Equation ◽  
One Dimension ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Delay Differential

In this paper, we provide a partition of the roots of a class of transcendental equation by using τ-D decomposition ,where τ>0,a>0,b<0 and the coefficient b is fixed.According to the partition, one can determine the stability domain of the equilibrium and get a Hopf bifurcation diagram that can provide the Hopf bifurcation curves in the-parameter space, for one dimension delay differential equation .

Sign in / Sign up

Export Citation Format

Share Document