A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations

2002 ◽  
Vol 60 (6) ◽  
pp. 507-512 ◽  
Author(s):  
Doǧan Kaya ◽  
Asif Yokus
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Numerical Comparison ◽  
Partial Differential ◽  
Linear And Nonlinear

scholarly journals Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Shailesh A. Bhanotar ◽  
Mohammed K. A. Kaabar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensions ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Linear And Nonlinear

In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. This method is generalized in the sense of conformable derivative. Important results and theorems concerning this method are discussed. A new algorithm is proposed to solve linear and nonlinear partial differential equations in three dimensions. Moreover, some examples are provided to verify the performance of the proposed algorithm. This method presents a wide applicability to solve nonlinear partial differential equations in the sense of conformable derivative.

scholarly journals Improvement of the Modified Decomposition Method for Handling Third-Order Singular Nonlinear Partial Differential Equations with Applications in Physics

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Nemat Dalir
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Differential Operators ◽  
Nonlinear Partial Differential Equations ◽  
Initial Value ◽  
Third Order ◽  
Partial Differential ◽  
The Third

The modified decomposition method (MDM) is improved by introducing new inverse differential operators to adapt the MDM for handling third-order singular nonlinear partial differential equations (PDEs) arising in physics and mechanics. A few case-study singular nonlinear initial-value problems (IVPs) of third-order PDEs are presented and solved by the improved modified decomposition method (IMDM). The solutions are compared with the existing exact analytical solutions. The comparisons show that the IMDM is effectively capable of obtaining the exact solutions of the third-order singular nonlinear IVPs.

scholarly journals Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Method ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
One Dimensional ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Sumudu Transform ◽  
Linear And Nonlinear

The conformable double Sumudu decomposition method (CDSDM) is a combination of decomposition method (DM) and a conformable double Sumudu transform. It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. Two examples are used to illustrate the method.

Solution Non Linear Partial Differential Equations By ZMA Decomposition Method

2021 ◽  
Vol 20 ◽  
pp. 712-716
Author(s):  
Zainab Mohammed Alwan
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Integral Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Adomian Decomposition

In this survey, viewed integral transformation (IT) combined with Adomian decomposition method (ADM) as ZMA- transform (ZMAT) coupled with (ADM) in which said ZMA decomposition method has been utilized to solve nonlinear partial differential equations (NPDE's).This work is very useful for finding the exact solution of (NPDE's) and this result is more accurate obtained with compared the exact solution obtained in the literature.

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