Regions of Stability in the Numerical Treatment of Volterra Integro-Differential Equations

1979 ◽  
Vol 16 (6) ◽  
pp. 890-910 ◽  
Author(s):  
Christopher T. H. Baker ◽  
Athena Makroglou ◽  
Edward Short
Keyword(s):  
Differential Equations ◽  
Numerical Treatment ◽  
Regions Of Stability

Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed M. Khader
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Convergence Order ◽  
Variable Order ◽  
Numerical Treatment ◽  
Dynamical Models ◽  
Fractional Modeling ◽  
Dynamics Problems

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

Numerical treatment of nonlinear mixed Volterra-Fredholm integro-differential equations of fractional order

2021 ◽  
Author(s):  
Zainidin Eshkuvatov ◽  
Zaid Laadjal ◽  
Shahrina Ismail
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Numerical Treatment

scholarly journals New Numerical Treatment for a Family of Two-Dimensional Fractional Fredholm Integro-Differential Equations

Algorithms ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 37
Author(s):  
Amer Darweesh ◽  
Marwan Alquran ◽  
Khawla Aghzawi
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Haar Wavelet ◽  
Two Dimensional ◽  
Numerical Treatment ◽  
Wavelet Method ◽  
New Approach ◽  
Robust Algorithm ◽  
Haar Wavelet Method ◽  
The Laplace Transform

In this paper, we present a robust algorithm to solve numerically a family of two-dimensional fractional integro differential equations. The Haar wavelet method is upgraded to include in its construction the Laplace transform step. This modification has proven to reduce the accumulative errors that will be obtained in case of using the regular Haar wavelet technique. Different examples are discussed to serve two goals, the methodology and the accuracy of our new approach.

Numerical treatment for the Nonlinear Fuzzy Differential Equations using Leapfrog Method

2015 ◽  
Vol 26 (1) ◽  
pp. 35-39
Author(s):  
S Sekar ◽  
◽  
K. Prabha vathi
Keyword(s):  
Differential Equations ◽  
Numerical Treatment
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