Determination of a source term in a partial differential equation arising in finance

2009 ◽  
Vol 88 (1) ◽  
pp. 131-140
Author(s):  
R. Sowrirajan ◽  
K. Balachandran
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Source Term ◽  
Partial Differential

scholarly journals Generating Functions for Bessel Functions

1959 ◽  
Vol 11 ◽  
pp. 148-155 ◽  
Author(s):  
Louis Weisner
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Generating Function ◽  
Lie Group ◽  
Generating Functions ◽  
Bessel Functions ◽  
Partial Differential ◽  
Systematic Determination ◽  
Image Position

On replacing the parameter n in Bessel's differential equation1.1by the operator y(∂/∂y), the partial differential equation Lu = 0 is constructed, where1.2This operator annuls u(x, y) = v(x)yn if, and only if, v(x) satisfies (1.1) and hence is a cylindrical function of order n. Thus every generating function of a set of cylindrical functions is a solution of Lu = 0.It is shown in § 2 that the partial differential equation Lu = 0 is invariant under a three-parameter Lie group. This group is then applied to the systematic determination of generating functions for Bessel functions, following the methods employed in two previous papers (4; 5).

scholarly journals A partial differential equation for pseudocontact shift

2014 ◽  
Vol 16 (37) ◽  
pp. 20184-20189 ◽  
Author(s):  
G. T. P. Charnock ◽  
Ilya Kuprov
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Probability Density ◽  
Unpaired Electron ◽  
Tensor Field ◽  
Source Term ◽  
Elliptic Partial Differential Equation ◽  
Three Dimensions ◽  
Pseudocontact Shift ◽  
Partial Differential

It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density.

scholarly journals Moving-Horizon Modulating Functions-Based Algorithm for Online Source Estimation in a First-Order Hyperbolic Partial Differential Equation

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Sharefa Asiri ◽  
Shahrazed Elmetennani ◽  
Taous-Meriem Laleg-Kirati
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Source Term ◽  
Environmental Changes ◽  
Estimation Methods ◽  
Hyperbolic Partial Differential Equation ◽  
Partial Differential ◽  
First Order ◽  
Source Estimation ◽  
Modulating Functions

In this paper, an online estimation algorithm of the source term in a first-order hyperbolic partial differential equation (PDE) is proposed. This equation describes heat transport dynamics in concentrated solar collectors where the source term represents the received energy. This energy depends on the solar irradiance intensity and the collector characteristics affected by the environmental changes. Control strategies are usually used to enhance the efficiency of heat production; however, these strategies often depend on the source term which is highly affected by the external working conditions. Hence, efficient source estimation methods are required. The proposed algorithm is based on modulating functions method (MFM) where a moving-horizon strategy is introduced. Numerical results are provided to illustrate the performance of the proposed estimator in open-and closed-loops.

On the Determination of the Natural Frequency of a Star-Shaped Membrane

1964 ◽  
Vol 68 (640) ◽  
pp. 274-275 ◽  
Author(s):  
Patricio A. Laura
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Unit Circle ◽  
Natural Frequency ◽  
Fundamental Mode ◽  
Polar Form ◽  
Complicated Shape ◽  
Partial Differential

SummaryThe natural frequency of the fundamental mode of star-shaped membranes whose boundary is given by an equation in polar form is determined. The boundary conditions are satisfied identically by conformally transforming the complicated shape onto a unit circle. The transformed partial differential equation is solved by two different collocation techniques.

scholarly journals Numerical Convergence Analysis of the Frank–Kamenetskii Equation

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 84
Author(s):  
Matthew Woolway ◽  
Byron A. Jacobs ◽  
Ebrahim Momoniat ◽  
Charis Harley ◽  
Dieter Britz
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Source Term ◽  
Steady State Solution ◽  
Partial Differential ◽  
Numerical Convergence ◽  
Termination Criteria ◽  
Newton Raphson ◽  
Spatial Discretisation

This work investigates the convergence dynamics of a numerical scheme employed for the approximation and solution of the Frank–Kamenetskii partial differential equation. A framework for computing the critical Frank–Kamenetskii parameter to arbitrary accuracy is presented and used in the subsequent numerical simulations. The numerical method employed is a Crank–Nicolson type implicit scheme coupled with a fourth order spatial discretisation as well as a Newton–Raphson update step which allows for the nonlinear source term to be treated implicitly. This numerical implementation allows for the analysis of the convergence of the transient solution toward the steady-state solution. The choice of termination criteria, numerically dictating this convergence, is interrogated and it is found that the traditional choice for termination is insufficient in the case of the Frank–Kamenetskii partial differential equation which exhibits slow transience as the solution approaches the steady-state. Four measures of convergence are proposed, compared and discussed herein.

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