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 Numerical Solution of European and American Option with Dividends using Finite Difference Methods

2020 ◽  
Vol 13 (13) ◽  
pp. 55-61
Author(s):  
Kedar Nath Uprety ◽  
Ganesh Prasad Panday
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Analytical Formula ◽  
Partial Differential ◽  
Dividend Payments ◽  
Fully Implicit ◽  
Black Scholes ◽  
Nicolson Scheme

Numerical methods form an important part of the pricing of financial derivatives where there is no closed form analytical formula. Black-Scholes equation is a well known partial differential equation in financial mathematics. In this paper, we have studied the numerical solutions of the Black-Scholes equation for European options (Call and Put) as well as American options with dividends. We have used different approximate to discretize the partial differential equation in space and explicit (Forward Euler’s), fully implicit with projected Successive Over-Relaxation (SOR) algorithm and Crank-Nicolson scheme for time stepping. We have implemented and tested the methods in MATLAB. Finally, some numerical results have been presented and the effects of dividend payments on option pricing have also been considered.

scholarly journals Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Dawei Cheng ◽  
Wenke Wang ◽  
Xi Chen ◽  
Zaiyong Zhang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Time Dependent ◽  
Analytic Method ◽  
Partial Differential ◽  
One Dimensional ◽  
Finite Analytic Method ◽  
Nonlinear Consolidation

For one-dimensional (1D) nonlinear consolidation, the governing partial differential equation is nonlinear. This paper develops the finite analytic method (FAM) to simulate 1D nonlinear consolidation under different time-dependent loading and initial conditions. To achieve this, the assumption of constant initial effective stress is not considered and the governing partial differential equation is transformed into the diffusion equation. Then, the finite analytic implicit scheme is established. The convergence and stability of finite analytic numerical scheme are proven by a rigorous mathematical analysis. In addition, the paper obtains three corrected semianalytical solutions undergoing suddenly imposed constant loading, single ramp loading, and trapezoidal cyclic loading, respectively. Comparisons of the results of FAM with the three semianalytical solutions and the result of FDM, respectively, show that the FAM can obtain stable and accurate numerical solutions and ensure the convergence of spatial discretization for 1D nonlinear consolidation.

Pressure Behavior During Polymer Flow in Petroleum Reservoirs

1982 ◽  
Vol 104 (2) ◽  
pp. 149-156 ◽  
Author(s):  
Chi U. Ikoku ◽  
H. J. Ramey
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
State Equations ◽  
Partial Differential ◽  
Dimensionless Radius ◽  
Dimensionless Pressure

This paper presents solutions of the nonlinear partial differential equation using the Douglas-Jones predictor-corrector method for the numerical solution of nonlinear partial differential equations. The results are presented in tabular form and as semilogarithmic and log-log type-curve graphs. Graphs of dimensionless pressure versus dimensionless radius also are presented. Compared to results from analytical solutions of the linear partial differential equation, the graphs have the same shape. The error introduced by the linearizing approximation is small for many values of the flow behavior index, n, and decreases as n tends to unity. Dimensionless pressure is a linear function of dimensionless radius to the power (1–n), near the well, as predicted by the steady-state equations. Also radius of investigation equation derived analytically agrees with results from numerical solutions.

scholarly journals Fractional variational iteration method for time-fractional non-linear functional partial differential equation having proportional delays

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 33-46 ◽  
Author(s):  
Durgun Dogan ◽  
Ali Konuralp
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Partial Differential ◽  
Data Set ◽  
Proportional Delays ◽  
Variational Iteration ◽  
Non Linear

In this paper, time-fractional non-linear partial differential equation with proportional delays are solved by fractional variational iteration method taking into account modified Riemann-Liouville fractional derivative. The numerical solutions which are calculated by using this method are better than those obtained by homotopy perturbation method and differential transform method with same data set and approximation order. On the other hand, to improve the solutions obtained by fractional variational iteration method, residual error function is used. With this additional process, the resulting approximate solutions are getting closer to the exact solutions. The results obtained by taking into account different values of variables in the domain are supported by compared tables and graphics in detail.

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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