System of integro-differential equations of convolution type with power nonlinearity

2021 ◽  
Vol 24 (3) ◽  
pp. 5-18
Author(s):  
S. N. Askhabov
Keyword(s):  
Differential Equations ◽  
Convolution Type ◽  
Power Nonlinearity

scholarly journals The Modified Sadik Decomposition Method to Solve a System of Nonlinear Fractional Volterra Integro-Differential Equations of Convolution type

2021 ◽  
Vol 20 ◽  
pp. 335-343
Author(s):  
Prapart Pue-On
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Explicit Form ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Initial Solution ◽  
Convolution Type ◽  
Adomian Decomposition

In this work, an incorporated form of Sadik transform and Adomian decomposition method which is called the Sadik decomposition method is presented. The method is applied to solve a system of nonlinear fractional Volterra integro-differential equations in the convolution form. To avoid collecting the noise terms that lead the method to fail for seeking the solution, the proposed method is modified by selecting a suitable initial solution. The obtained results are expressed in the explicit form of a power series with easily computable terms. In addition, illustrative examples are shown to demonstrate the effectiveness of the method.

scholarly journals Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Elhassan Eljaoui ◽  
Said Melliani ◽  
L. Saadia Chadli
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Convolution Type ◽  
Convolution Product ◽  
Fuzzy Mapping ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Improper Integral ◽  
Convolution Formula

We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with kernel of convolution type. Then, we report and correct an error in the article by Salahshour et al. dealing with the same topic.

scholarly journals An ultraspherical spectral method for linear Fredholm and Volterra integro-differential equations of convolution type

2018 ◽  
Vol 39 (4) ◽  
pp. 1727-1746 ◽  
Author(s):  
Nicholas Hale
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Spectral Method ◽  
Linear Complexity ◽  
Convolution Type ◽  
New Technique ◽  
Legendre Series ◽  
Banded Linear Systems ◽  
A New Technique

Abstract The Legendre-based ultraspherical spectral method for ordinary differential equations (Olver, S. & Townsend, A. (2013) A fast and well-conditioned spectral method. SIAM Rev., 55, 462–489.) is combined with a formula for the convolution of two Legendre series (Hale, N. & Townsend, A. (2014a) An algorithm for the convolution of Legendre series. SIAM J. Sci. Comput., 36, A1207–A1220.) to produce a new technique for solving linear Fredholm and Volterra integro-differential equations with convolution-type kernels. When the kernel and coefficient functions are sufficiently smooth, then the method is spectrally accurate and the resulting almost-banded linear systems can be solved with linear complexity.

scholarly journals An Approximated Solutions for nth Order Linear Delay Integro-Differential Equations of Convolution Type Using B-Spline Functions and Weddle Method

2014 ◽  
Vol 11 (1) ◽  
pp. 166-177
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Convolution Type ◽  
Spline Functions ◽  
Exact Results ◽  
B Spline ◽  
Order Linear ◽  
Linear Delay

The paper is devoted to solve nth order linear delay integro-differential equations of convolution type (DIDE's-CT) using collocation method with the aid of B-spline functions. A new algorithm with the aid of Matlab language is derived to treat numerically three types (retarded, neutral and mixed) of nth order linear DIDE's-CT using B-spline functions and Weddle rule for calculating the required integrals for these equations. Comparison between approximated and exact results has been given in test examples with suitable graphing for every example for solving three types of linear DIDE's-CT of different orders for conciliated the accuracy of the results of the proposed method.

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