scholarly journals A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 949 ◽  
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub ◽  
Yahya T. Abdalla ◽  
Adem Kılıçman
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Laplace Decomposition Method

The purpose of this article is to obtain the exact and approximate numerical solutions of linear and nonlinear singular conformable pseudohyperbolic equations and conformable coupled pseudohyperbolic equations through the conformable double Laplace decomposition method. Further, the numerical examples were provided in order to demonstrate the efficiency, high accuracy, and the simplicity of present method.

scholarly journals Application of double natural decomposition method for solving singular one dimensional Boussinesq equation

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4389-4401 ◽  
Author(s):  
Hassan Gadain
Keyword(s):  
Decomposition Method ◽  
Boussinesq Equation ◽  
Adomian Decomposition Method ◽  
Boussinesq Equations ◽  
Science And Engineering ◽  
Transform Method ◽  
One Dimensional ◽  
Adomian Decomposition ◽  
Linear And Nonlinear ◽  
Natural Decomposition

In this work, a combined form of the double Natural transform method with the Adomian decomposition method is developed for analytic treatment of the linear and nonlinear singular one dimensional Boussinesq equations. Two examples are provided to illustrate the simplicity and reliability of this method. Moreover, the results show that the proposed method is effective and is easy to implement for certain problems in science and engineering.

scholarly journals Modified Modelling for Heat Like Equations within Caputo Operator

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 2002 ◽  
Author(s):  
Hassan Khan ◽  
Adnan Khan ◽  
Maysaa Al-Qurashi ◽  
Rasool Shah ◽  
Dumitru Baleanu
Keyword(s):  
Exact Solution ◽  
Present Method ◽  
Numerical Solutions ◽  
Graphical Representation ◽  
Close Contact ◽  
Form Solution ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Closed Form Solutions ◽  
Novel Approach

The present paper is related to the analytical solutions of some heat like equations, using a novel approach with Caputo operator. The work is carried out mainly with the use of an effective and straight procedure of the Iterative Laplace transform method. The proposed method provides the series form solution that has the desired rate of convergence towards the exact solution of the problems. It is observed that the suggested method provides closed-form solutions. The reliability of the method is confirmed with the help of some illustrative examples. The graphical representation has been made for both fractional and integer-order solutions. Numerical solutions that are in close contact with the exact solutions to the problems are investigated. Moreover, the sample implementation of the present method supports the importance of the method to solve other fractional-order problems in sciences and engineering.

scholarly journals A New Coupled Fractional Reduced Differential Transform Method for the Numerical Solutions of(2+1)-Dimensional Time Fractional Coupled Burger Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
S. Saha Ray
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Present Method ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Linear And Nonlinear

A very new technique, coupled fractional reduced differential transform, has been implemented to obtain the numerical approximate solution of (2 + 1)-dimensional coupled time fractional burger equations. The fractional derivatives are described in the Caputo sense. By using the present method we can solve many linear and nonlinear coupled fractional differential equations. The obtained results are compared with the exact solutions. Numerical solutions are presented graphically to show the reliability and efficiency of the method.

scholarly journals On a nonlinear singular one-dimensional parabolic equation and double Laplace decomposition method

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668653 ◽  
Author(s):  
Hassan Eltayeb Gadain ◽  
Imed Bachar
Keyword(s):  
Parabolic Equation ◽  
Laplace Transform ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method

In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals A bridging method for global optimization

1999 ◽  
Vol 41 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Y. Liu ◽  
K. L. Teo
Keyword(s):  
Global Optimization ◽  
Differentiable Function ◽  
Numerical Solutions ◽  
Finite Interval ◽  
Optimization Problems ◽  
Optimal Solutions ◽  
Numerical Examples ◽  
One Dimensional ◽  
Differentiable Functions ◽  
Global Optimal

AbstractIn this paper a bridging method is introduced for numerical solutions of one-dimensional global optimization problems where a continuously differentiable function is to be minimized over a finite interval which can be given either explicitly or by constraints involving continuously differentiable functions. The concept of a bridged function is introduced. Some properties of the bridged function are given. On this basis, several bridging algorithm are developed for the computation of global optimal solutions. The algorithms are demonstrated by solving several numerical examples.

scholarly journals Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Limei Yan
Keyword(s):  
Laplace Transform ◽  
Numerical Solutions ◽  
Convergent Series ◽  
Space Time ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Promising Tool ◽  
The Laplace Transform ◽  
Fokker Planck Equations ◽  
Fokker Planck

A relatively new iterative Laplace transform method, which combines two methods; the iterative method and the Laplace transform method, is applied to obtain the numerical solutions of fractional Fokker-Planck equations. The method gives numerical solutions in the form of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and straightforward when applied to space-time fractional Fokker-Planck equations. The method provides a promising tool for solving space-time fractional partial differential equations.

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.

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