Applications of Double Fuzzy Sumudu Adomain Decompositon Method for Two-dimensional Volterra Fuzzy Integral Equations

Abstract

In this paper, we combine double Sumudu transform with Adomian decomposition method to solve two dimensional fuzzy convolution Volterra integral equations. We give some definition for fuzzy number, fuzzy valued function which are prerequest for combine the double fuzzy Sumudu transform with Adomian decomposition transform method. We describe the method and finally, numerical examples are given to illustrate the efficiency and applicability of our method.

The Possible Solutions for the two KdV-type Equations Using a Semi-analytical Kamal-iteration Method

“…However, the error of the approximate solution of the classical iterations method is higher than the error of the modified iterations method. The error induced by the polynomial terms of degree higher than the iteration order n = 3 which cause high noise in the calculation, see Figure (6). Removing the noise terms in the modified iterations method leads to better convergence towards the exact solution, see Figure (3).…”

“…Figure (6) shows the sketch of w 3 (x, t) when n = 2. In addition, as n → ∞, the w n+1 has unnecessary (noise) terms which makes the approximate solution looks divergent from the exact solution.…”

“…However, all these transforms cannot be used directly if they are employed for the nonlinear homogeneous or nonhomogeneous ordinary and PDEs, because there are no transforms for the nonlinear part. For that reason, some researchers have used the integral transform with the help of decomposition, variational methods and others to solve this problem [6,23,24].…”

Approximate Analytical Solution of Fuzzy Linear Volterra Integral Equation via Elzaki ADM

“…Laplace ADM was used by Ullah et al [7] to propose a solution to fuzzy Volterra integral equations. Applications of the double Sumudu ADM for 2D fuzzy Volterra integral equations were announced by Alidema [8].…”

“…and exact solutions for lower and upper bounds at 𝒂 = 1, 3, 5, 7, and 9 regarding Example 1.Example 2. Considered the fuzzy linear Volterra integral equation as follows:𝜃(𝑦, 𝛼 ) = ℎ(𝑦, 𝛼 ) + 𝑘(𝑦, 𝑠) 𝜃(𝑠, 𝛼 )𝑑𝑠 (8).…”