Numerical methods for a partial differential equation with spatial delay arising in option pricing under hard-to-borrow model

2018 ◽  
Vol 76 (9) ◽  
pp. 2129-2140 ◽  
Author(s):  
Yong Chen ◽  
Jingtang Ma
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Methods ◽  
Option Pricing ◽  
Partial Differential

scholarly journals Numerical methods for the multiplicative partial differential equations

2017 ◽  
Vol 15 (1) ◽  
pp. 1344-1350
Author(s):  
Muhammet Yazıcı ◽  
Harun Selvitopi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Methods ◽  
Error Estimation ◽  
Truncation Error ◽  
Numerical Solutions ◽  
Partial Differential ◽  
The Matrix ◽  
The Stability ◽  
Truncation Error Estimation

Abstract We propose the multiplicative explicit Euler, multiplicative implicit Euler, and multiplicative Crank-Nicolson algorithms for the numerical solutions of the multiplicative partial differential equation. We also consider the truncation error estimation for the numerical methods. The stability of the algorithms is analyzed by using the matrix form. The result reveals that the proposed numerical methods are effective and convenient.

scholarly journals Modal Analysis of Vibration of Euler-Bernoulli Beam Subjected to Concentrated Moving Load

2020 ◽  
pp. 2324-2334
Author(s):  
Usman M. A ◽  
Makinde T. A. ◽  
Daniel D. O.
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Methods ◽  
Modal Analysis ◽  
Series Solution ◽  
Moving Load ◽  
Bernoulli Beam ◽  
Partial Differential ◽  
Concentrated Load ◽  
Euler Bernoulli Beam

This paper investigates the modal analysis of vibration of Euler-Bernoulli beam subjected to concentrated load. The governing partial differential equation was analysed to determine the behaviour of the system under consideration. The series solution and numerical methods were used to solve the governing partial differential equation. The results revealed that the amplitude increases as the length of the beam increases. It was also found that the response amplitude increases as the foundation increases at fixed length of the beam.

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