scholarly journals Numerical study of time-fractional fourth-order differential equations with variable coefficients

2011 ◽  
Vol 23 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Nasir-Uddin Khan ◽  
Muhammad Ayaz ◽  
Amir Mahmood ◽  
Noor Fatima
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Numerical Study ◽  
Variable Coefficients

The Solution of the Variable Coefficients Fourth-Order Parabolic Partial Differential Equations by the Homotopy Perturbation Method

2009 ◽  
Vol 64 (7-8) ◽  
pp. 420-430 ◽  
Author(s):  
Mehdi Dehghan ◽  
Jalil Manafian
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Fourth Order ◽  
Homotopy Perturbation Method ◽  
Variable Coefficients ◽  
Parabolic Partial Differential Equation ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Homotopy Perturbation

AbstractIn this work, the homotopy perturbation method proposed by Ji-Huan He [1] is applied to solve both linear and nonlinear boundary value problems for fourth-order partial differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solution to show the efficiency of the method. The results show that the homotopy perturbation method is of high accuracy and efficient for solving the fourth-order parabolic partial differential equation with variable coefficients. The results show also that the introduced method is a powerful tool for solving the fourth-order parabolic partial differential equations.

scholarly journals An Improved Criterion for the Oscillation of Fourth-Order Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 610 ◽  
Author(s):  
Omar Bazighifan ◽  
Marianna Ruggieri ◽  
Andrea Scapellato
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Asymptotic Properties ◽  
Variable Coefficients ◽  
Averaging Technique ◽  
Integral Averaging Technique ◽  
Oscillation Of Solutions

The main purpose of this manuscript is to show asymptotic properties of a class of differential equations with variable coefficients r ν w ‴ ν β ′ + ∑ i = 1 j q i ν y κ g i ν = 0 , where ν ≥ ν 0 and w ν : = y ν + p ν y σ ν . By using integral averaging technique, we get conditions to ensure oscillation of solutions of this equation. The obtained results improve and generalize the earlier ones; finally an example is given to illustrate the criteria.

scholarly journals Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yesuf Obsie Mussa ◽  
Ademe Kebede Gizaw ◽  
Ayana Deressa Negassa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform

In this study, the fractional reduced differential transform method (FRDTM) is employed to solve three-dimensional fourth-order time-fractional parabolic partial differential equations with variable coefficients. The fractional derivative used in this study is in the Caputo sense. A few important lemmas which are essential to solve the problems using the proposed method are proved. The novelty of this method is that it uses appropriate initial conditions and finds the solution to the problems without any discretization, linearization, perturbation, or any restrictive assumptions. Two numerical examples are considered in order to validate the efficiency and reliability of the method. Furthermore, the FRDTM solution when α = 1 is compared with other analytical methods available in the existing literature. Computational results are shown in tables and graphs. The obtained results revealed that the method is capable and simple to solve fractional partial differential equations. The software used for the calculations in this study is Mathematica 7.

scholarly journals Two non-elementary integral functions defined using central factorial powers

2015 ◽  
Vol 23 ◽  
pp. 98
Author(s):  
T.P. Goy
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Variable Coefficients ◽  
Elementary Functions ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

We study two new real-valued non-elementary functions generated by central factorial powers. Graphs of such functions are plotted and some of their properties are proved. It is also shown that new integral functions are solutions of fourth order linear ordinary differential equations with variable coefficients.

Effects of multiplicative noise on the Duffing oscillator with variable coefficients and its integral of motion

2020 ◽  
Vol 31 (07) ◽  
pp. 2050095
Author(s):  
E. Urenda-Cázares ◽  
A. Gallegos ◽  
R. Jaimes-Reátegui
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Multiplicative Noise ◽  
Duffing Oscillator ◽  
Variable Coefficients ◽  
Kutta Method ◽  
Integral Of Motion ◽  
Runge Kutta Method

In this work, we implement multiplicative noise to the Duffing oscillator with variable coefficients. The stochastic differential equations are solved using the fourth-order Runge–Kutta method with the Box-Müller algorithm and the corresponding integral of motion is obtained. Some numerical experiments are performed and the results show that the integral of motion is highly unaffected by the multiplicative noise.

Sign in / Sign up

Export Citation Format

Share Document