scholarly journals Numerical Simulations for the Space-Time Variable Order Nonlinear Fractional Wave Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Nasser Hassan Sweilam ◽  
Taghreed Abdul Rahman Assiri
Keyword(s):  
Wave Equation ◽  
Truncation Error ◽  
Source Term ◽  
Numerical Test ◽  
Space Time ◽  
Variable Order ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Variable Order Fractional Derivative ◽  
Explicit Finite Difference Method

The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered. The concept of variable order fractional derivative is considered in the sense of Caputo. The stability analysis and the truncation error of the method are discussed. To demonstrate the effectiveness of the method, some numerical test examples are presented.

Numerical studies for the variable-order nonlinear fractional wave equation

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
N. Sweilam ◽  
M. Khader ◽  
H. Almarwm
Keyword(s):  
Wave Equation ◽  
Stability Analysis ◽  
Numerical Scheme ◽  
Numerical Test ◽  
Variable Order ◽  
Fractional Wave Equation ◽  
Numerical Studies ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Explicit Finite Difference Method

AbstractIn this paper, the explicit finite difference method (FDM) is used to study the variable order nonlinear fractional wave equation. The fractional derivative is described in the Riesz sense. Special attention is given to study the stability analysis and the convergence of the proposed method. Numerical test examples are presented to show the efficiency of the proposed numerical scheme.

scholarly journals Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Li Wu ◽  
Zhouhong Li ◽  
Yuan Zhang ◽  
Binggeng Xie
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Land Reclamation ◽  
Variable Order ◽  
Transformation Rate ◽  
Complex Behavior ◽  
Bifurcation Parameter ◽  
Type Transformation ◽  
The Stability ◽  
Variable Order Fractional Derivative

In this paper, a fractional-order land model with Holling-II type transformation rate and time delay is investigated. First of all, the variable-order fractional derivative is defined in the Caputo type. Second, by applying time delay as the bifurcation parameter, some criteria to determine the stability and Hopf bifurcation of the model are presented. It turns out that the time delay can drive the model to be oscillatory, even when its steady state is stable. Finally, one numerical example is proposed to justify the validity of theoretical analysis. These results may provide insights to the development of a reasonable strategy to control land-use change.

scholarly journals Error Analysis of An Explicit Finite Difference Approximation for the Space Fractional Wave Equations

2012 ◽  
Vol 17 (2) ◽  
pp. 245
Author(s):  
N.H. Sweilam ◽  
T.A. Assiri
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Error Analysis ◽  
Wave Equations ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Explicit Finite Difference ◽  
The Stability

In this paper, the space fractional wave equation (SFWE) is numerically studied, where the fractional derivative is defined in the sense of Caputo. An explicit finite difference approximation (EFDA) for SFWE is presented. The stability and the error analysis of the EFDA are discussed. To demonstrate the effectiveness of the approximated method, some test examples are presented.   

scholarly journals Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives

2016 ◽  
Vol 26 (3) ◽  
pp. 429-435 ◽  
Author(s):  
Roman I. Parovik
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Fractional Derivatives ◽  
Stability And Convergence ◽  
Variable Order ◽  
The Difference ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Variable Order Fractional Derivatives

Abstract The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.

Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative

2017 ◽  
Vol 9 (4) ◽  
pp. 990-1011 ◽  
Author(s):  
N. H. Sweilam ◽  
M. M. Abou Hasan
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Space Variable ◽  
Weighted Average ◽  
Variable Order ◽  
Computationally Efficient ◽  
Fractional Schrödinger Equation ◽  
The Stability ◽  
Variable Order Fractional Derivative ◽  
Fractional Schrodinger Equation

AbstractIn this paper the space variable-order fractional Schrödinger equation (VOFSE) is studied numerically, where the variable-order fractional derivative is described here in the sense of the quantum Riesz-Feller definition. The proposed numerical method is the weighted average non-standard finite difference method (WANSFDM). Special attention is given to study the stability analysis and the convergence of the proposed method. Finally, two numerical examples are provided to show that this method is reliable and computationally efficient.

scholarly journals Super-Time-Stepping Scheme for Option Pricing

2020 ◽  
Vol 13 (13) ◽  
pp. 51-54
Author(s):  
Kedar Nath Uprety ◽  
Harithar Khanal ◽  
Ananta Upreti
Keyword(s):  
Option Pricing ◽  
Euler Method ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Time Stepping ◽  
Black Scholes ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Explicit Finite Difference Method

We solve the Black - Scholes equation for option pricing numerically using an Explicit finite difference method. To overcome the stability restriction of the explicit scheme for parabolic partial differential equations in the time step size Courant-Friedrichs-Lewy (CFL) condition, we employ a Super Time Stepping (STS) strategy based on modified Chebyshev polynomial. The numerical results show that the STS scheme boasts of large efficiency gains compared to the standard explicit Euler method.

scholarly journals SPACE-TIME SPECTRAL COLLOCATION ALGORITHM FOR THE VARIABLE-ORDER GALILEI INVARIANT ADVECTION DIFFUSION EQUATIONS WITH A NONLINEAR SOURCE TERM

2017 ◽  
Vol 22 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Mohamed A. Abd-Elkawy ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Source Term ◽  
Dimensional Space ◽  
Space Time ◽  
Variable Order ◽  
Spectral Collocation ◽  
Nonlinear Source ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Collocation Technique ◽  
Collocation Scheme

This paper presents a space-time spectral collocation technique for solving the variable-order Galilei invariant advection diffusion equation with a nonlinear source term (VO-NGIADE). We develop a collocation scheme to approximate VONGIADE by means of the shifted Jacobi-Gauss-Lobatto collocation (SJ-GL-C) and shifted Jacobi-Gauss-Radau collocation (SJ-GR-C) methods. We successfully extend the proposed technique to solve the two-dimensional space VO-NGIADE. The discussed numerical tests illustrate the capability and high accuracy of the proposed methodologies.

Sign in / Sign up

Export Citation Format

Share Document