Nonlinear fractional arctic systems

In this contribution, the nonlinear fractional arctic sea ice model is given, and the solution of the model was obtained using a new proposed modified Adomian decomposition method. The result is compared with the integer-order model, and we observed that a model with fractional order gives a better result. We also observed that the effect of climate change on arctic sea ice could lead to a large-scale sea ice melting with sea-level rise for several meters, which could pose a major threat to low-lying island nations and coastal areas.

Numerical solution of Drinfeld–Sokolov–Wilso system by using modified Adomian decomposition method

<p class="Char">In this paper, the modified Adomian decomposition method (MADM) is usedto solve different types of differential equations, one of the numerical analysis methods for solving non linear partial differential equations (Drinfeld–Sokolov–Wilson system) and short (DSWS) that occur in shallow water flows. A Genetic Algorithm was used to find the optimal value for the parameter (a). We numerically solved the system (DSWS) and compared the result to the exact solution. When the value of it is low and close to zero, the MADM provides an excellent approximation to the exact solution. As well as the lower value of leads to the numerical algorithm of (MADM) approaching the real solution. Finally, found the optimal value when a=-10 by using the Genetic Algorithm (G-MADM). All the computations were carried out with the aid of Maple 18 and Matlab to find the parameter value (a) by using the genetic algorithm as well as to figures drawing. The errors in this paper resulted from cut errors and mean square errors.</p>

Numerical Solution of Integral Equation by using New Modified Adomian Decomposition Method and Newton Raphson Methods

In this paper, we discuss the numerical solution of Adomian decomposition method and Taylor’s expansion method in Volterra linear integral equation. And we apply modified Adomian decomposition method and Newton Raphson method in Volterra nonlinear integral equation with the help of example and estimated an error in MATLAB 13 versions.

Mathematical Modelling in Engineering with Integral Transforms via Modified Adomian Decomposition Method

In this work three integral transforms through modified Adomian decomposition method (ADM) are proposed to obtain the approximate analytical solution of different types of mathematical models arising in physical problems. These transformations are applied for both homogeneous and non-homogeneous linear differential equations. The efficiency and accuracy of the proposed methods are implemented through higher order non-homogeneous ordinary differential equations. Numerical tests are reported for applicability of the current scheme based on different transformations and compared with exact solutions.

Modified Adomian Decomposition Method for the Solution of Integro-Differential Equations

This paper is concerned with modification of the Adomian Decomposition Method for solving linear and non-linear Volterra and Volterra-Fredholm Integro-Differential equations. The Modified form of ADM was carried out by replacing the Adomian polynomials constructed in the conventional Adomian Decomposition Method with the constructed canonical polynomials. The modified Adomian Decomposition Method was applied to solve some existing example. The results obtained using the newly modified ADM proved superior when compared with the conventional ADM.

Optimal Parameters for Nonlinear Hirota-Satsuma Coupled KdV System by Using Hybrid Firefly Algorithm with Modified Adomian Decomposition

In this paper, several parameters of the non-linear Hirota-Satsuma coupled KdV system were estimated using a hybrid between the Firefly Algorithm (FFA) and the Modified Adomian decomposition method (MADM). It turns out that optimal parameters can significantly improve the solutions when using a suitably selected fitness function for this problem. The results obtained show that the approximate solutions are highly compatible with the exact solutions and that the hybrid method FFA_MADM gives higher efficiency and accuracy compared to the classic MADM method.

Solution of Two-Point Linear and Nonlinear Boundary Value Problems with Neumann Boundary Conditions Using a New Modified Adomian Decomposition Method

In this paper, we present the New Modified Adomian Decomposition Method which is a modification of the Modified Adomian Decomposition Method. The new method incorporates the inverse linear operator theorem into the modified Adomian decomposition method for the calculation of u0. Six linear and nonlinear boundary value problems with Neumann conditions are solved in order to test the method. The results show that the method is effective.