scholarly journals Analysis of the stability of the linear boundary condition for the Black–Scholes equation

2004 ◽  
Vol 8 (1) ◽  
pp. 65-92 ◽  
Author(s):  
Heath Windcliff ◽  
Peter Forsyth ◽  
Ken Vetzal
Keyword(s):  
Boundary Condition ◽  
Linear Boundary ◽  
Linear Boundary Condition ◽  
Black Scholes ◽  
The Stability

scholarly journals Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Darae Jeong ◽  
Seungsuk Seo ◽  
Hyeongseok Hwang ◽  
Dongsun Lee ◽  
Yongho Choi ◽  
...  
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Linear Boundary ◽  
Partial Differential ◽  
Various Boundary Conditions ◽  
Linear Boundary Condition ◽  
Black Scholes

We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. We use a finite difference method to numerically solve the equation. To show the efficiency of the given boundary condition, several numerical examples are presented. In numerical test, we investigate the effect of the domain sizes and compare the effect of various boundary conditions with pointwise error and root mean square error. Numerical results show that linear boundary condition is accurate and efficient among the other boundary conditions.

scholarly journals Homogenization of a Conductive and Radiative Heat Transfer Problem, Simulation With CAST3M

2005 ◽  
Author(s):  
K. El Ganaoui ◽  
G. Allaire
Keyword(s):  
Boundary Condition ◽  
Radiative Heat ◽  
Transfer Problem ◽  
Computer Code ◽  
Homogenization Theory ◽  
Linear Boundary ◽  
Mathematical Study ◽  
Linear Boundary Condition ◽  
The Core ◽  
Homogenous Medium

We are interested in conductive and radiative transfer of energy in the core of gas cooled reactors. Two scales characterize the problem: macroscopic and microscopic. We want to consider the domain like an equivalent homogenous medium. So we use homogenization theory to compute the effective macroscopic properties which take into account the microscopic structure. We first present a full mathematical study of a simpler conduction problem with non linear boundary condition and its simulation with the CEA’s (French Atomic Energy Commissariat) computer code CAST3M. Then we present the homogenization of the real physical problem (including radiative boundary condition).

The theory of symmetrical gravity waves of finite amplitude. I

1951 ◽  
Vol 208 (1095) ◽  
pp. 475-486 ◽  
Keyword(s):  
Boundary Condition ◽  
Gravity Waves ◽  
Finite Amplitude ◽  
Breaking Wave ◽  
Two Dimensional ◽  
Linear Boundary ◽  
Dimensional Problem ◽  
Infinite Depth ◽  
Linear Boundary Condition ◽  
Small Parameters

The two-dimensional problem of symmetric finite amplitude gravity waves in an incompressible fluid of infinite depth is treated by a method which first involves satisfying a non-linear boundary condition exactly. The higher approximations are obtained by the method of small parameters. The breaking-wave conditions are discussed and expressions are given for the free-surface equation, the kinetic and the potential energies of the fluid.

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