scholarly journals Optimization of the Solution of a Dispersion Model

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 318
Author(s):  
Alexandru-Nicolae Dimache ◽  
Ghiocel Groza ◽  
Marilena Jianu ◽  
Sorin Perju ◽  
Laurențiu Rece ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
General Solution ◽  
Analytic Solution ◽  
Least Squares Method ◽  
Dispersion Model ◽  
Tracer Test ◽  
Main Step ◽  
Uniqueness Of The Solution ◽  
Dispersion Number

The study of the combination of chemical kinetics with transport phenomena is the main step for reactor design. It is possible to deviate from the model behaviour, the cause of which may be fluid channelling, fluid recirculation, or creation of stagnant regions in the vessel, by using a dispersion model. In this paper, the known general solution of the dispersion model for closed vessels is given in a new, straightforward form. In order to improve the classical theoretical solution, a hybrid of analytical and numerical methods is used. It is based on the general analytic solution and the least-squares method by fitting the results of a tracer test carried out on the vessel with the values of the analytic solution. Thus, the accuracy of the estimation for the vessel dispersion number is increased. The presented method can be used to similar problems modelled by a partial differential equation and some boundary conditions which are not sufficient to ensure the uniqueness of the solution.

Non-Uniqueness of The Solution to a Generalized Dirichlet Problem

1974 ◽  
Vol 17 (4) ◽  
pp. 605-606
Author(s):  
E. L. Koh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Unique Solution ◽  
Partial Differential ◽  
Uniqueness Of The Solution ◽  
Image Position ◽  
Generalized Dirichlet

It is generally known [1] that the singular partial differential equationmay not have a unique solution because of the existence of nontrivial representations of zero.1

scholarly journals Three ways to solve for bond prices in the Vasicek model

2004 ◽  
Vol 8 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Rogemar S. Mamon
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytic Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Bond Pricing ◽  
Rate Process ◽  
Bond Price ◽  
Martingale Approach ◽  
Forward Measure

Three approaches in obtaining the closed-form solution of the Vasicek bond pricing problem are discussed in this exposition. A derivation based solely on the distribution of the short rate process is reviewed. Solving the bond price partial differential equation (PDE) is another method. In this paper, this PDE is derived via a martingale approach and the bond price is determined by integrating ordinary differential equations. The bond pricing problem is further considered within the Heath-Jarrow-Morton (HJM) framework in which the analytic solution follows directly from the short rate dynamics under the forward measure.

The spectrum of the self-adjoint partial differential equation in any domain

1933 ◽  
Vol 29 (1) ◽  
pp. 23-44
Author(s):  
S. W. P. Steen
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Riemann Surface ◽  
General Solution ◽  
Boundary Conditions ◽  
Continuous Functions ◽  
The Self ◽  
Partial Differential ◽  
Image Position ◽  
Dimensional Domain

The object of this paper is to obtain the general solution to the self-adjoint partial differential equation in n dimensionswhere pij, q and ρ and bounded, continuous functions of (x1,…, xn) in a domain D and on its boundary, and where ∑pijXiXj≥0 for all (x1,…, xn) of D and all X1,…, Xn. The domain D is an n-dimensional domain and may be either the whole or part of a Riemann surface space of n dimensions. Its boundary is to consist of any number, zero, finite or enumerable, of continuous continua of n − 1 dimensions. These terms will be explained in paragraph II. The solution u = u(x1,…, xn; t) will be valid for (x1,…, xn) in D and t ≥ 0, and will satisfy boundary conditions of the type or similar, these conditions becoming identical at any part of the boundary of D that lies at infinity.

MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 08 (02) ◽  
pp. 271-294 ◽  
Author(s):  
B. BOUFOUSSI ◽  
N. MRHARDY
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Partial Differential Equation ◽  
Yosida Approximation ◽  
Partial Differential ◽  
Doubly Stochastic ◽  
Uniqueness Of The Solution

In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic partial differential equation.

Uniqueness of the Solution to a Difference-Partial Differential Equation for Finance

2003 ◽  
Vol 13 (07) ◽  
pp. 919-943
Author(s):  
C. Mancini
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rate ◽  
Jump Diffusion ◽  
Market Model ◽  
Contingent Claim ◽  
Partial Differential ◽  
Financial Model ◽  
Diffusion Modelling ◽  
Uniqueness Of The Solution

In this paper we study a difference partial differential equation, arising from a financial model, whose solution represents the price of a security linked to a dividend-paying stock. The market model consists of a jump-diffusion process modelling the stock evolution and an independent diffusion modelling the stochastic spot interest rate. We establish the desirable property of the uniqueness of solution to the equation and, since the specialized model is complete, we can consistently price any contingent claim.

Convergence and Error Analysis of Series Solution of Nonlinear Partial Differential Equation

2018 ◽  
Vol 7 (4) ◽  
pp. 303-308 ◽  
Author(s):  
Prince Singh ◽  
Dinkar Sharma
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Error Analysis ◽  
Series Solution ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential ◽  
Uniqueness Of The Solution ◽  
Established Fact ◽  
Sumudu Transforms

Abstract A hybrid method of Sumudu transforms and homotopy perturbation method (HPM) is used to solve nonlinear partial differential equation. Here the nonlinear terms are handled with He’s polynomial to obtain the series solution. But, for the authenticity of the obtained solution, the condition of convergence and uniqueness of the solution is derived. The facts are obtained in reference to convergence and error analysis of this solution. Finally, the established fact is supported by finding solution of two well known equations Newell-Whitehead Segel and Fisher’s equation

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