scholarly journals On the solutions of some boundary value problems by using differential transformation method with convolution terms

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 917-928 ◽  
Author(s):  
Adem Kılıçman ◽  
Ömer Altun
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Partial Differential Operator ◽  
Transformation Method ◽  
New Method ◽  
Differential Transformation Method ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transformation

In this study, we consider some boundary value problems by using the differential transformation method with convolutions term. Further, we also propose a new method to solve the differential equations having singularity by using the convolution. In this new method when the operator has some singularities then we multiply the partial differential operator with continuously differential functions by using the convolution in order to regularize the singularity. Then the differential transform method will be applied to the new partial differential equations that might also have some fractional order.

scholarly journals DIFFERENTIAL TRANSFORMATION METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

2016 ◽  
Vol 78 (6-4) ◽  
Author(s):  
Che Haziqah Che Hussin ◽  
Arif Mandangan ◽  
Adem Kilicman ◽  
Muhamad Azlan Daud ◽  
Nurliyana Juhan
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Relative Error ◽  
Decomposition Method ◽  
Boundary Value ◽  
Transformation Method ◽  
Sixth Order ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Absolute Relative Error

In this study, sixth-order boundary value problems for linear and nonlinear differential equations have been solved by using Differential Transformation Method (DTM). The numerical solutions are given in several examples. For each example, the solution given by DTM is compared with the exact solution. Absolute relative error (ARE) for each iteration can be computed. Therefore, the maximum absolute relative error (MARE) of the DTM can be obtained. To show that the solution given by the DTM has higher level of accuracy, the absolute relative error of the DTM has been compared with the other methods such as Adomian decomposition method with Green’s function, modified decomposition method (MDM), homotopy perturbation method (HPM), Variational Iteration Method (VIM) and Quintic B-Spline Collocation Method. Comparison graphs are given at the end of this paper. The obtained result shows that the proposed method is able to provide better approximation in term of accuracy.

scholarly journals On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Che Haziqah Che Hussin ◽  
Adem Kiliçman
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Transformation Method ◽  
Higher Order ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Adomian Decomposition

We study higher-order boundary value problems (HOBVP) for higher-order nonlinear differential equation. We make comparison among differential transformation method (DTM), Adomian decomposition method (ADM), and exact solutions. We provide several examples in order to compare our results. We extend and prove a theorem for nonlinear differential equations by using the DTM. The numerical examples show that the DTM is a good method compared to the ADM since it is effective, uses less time in computation, easy to implement and achieve high accuracy. In addition, DTM has many advantages compared to ADM since the calculation of Adomian polynomial is tedious. From the numerical results, DTM is suitable to apply for nonlinear problems.

scholarly journals Solusi Persamaan Schrodinger dengan Menggunakan Metode Transformasi Diferensial

2021 ◽  
Vol 4 (1) ◽  
pp. 47
Author(s):  
Muhammad Abdy ◽  
Hisyam Ihsan ◽  
Dhea Ayu Rossyana Dewi
Keyword(s):  
Partial Differential Equations ◽  
Schrödinger Equation ◽  
Differential Equations ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Partial Differential ◽  
Differential Transformation ◽  
Initial Values

Abstrak. Penelitian ini membahas tentang solusi persamaan diferensial parsial linier yaitu persamaan Schrodinger. Solusi persamaan ini dilakukan dengan menggunakan metode transformasi diferensial yang merupakan metode semi-numerik-analitik yang dapat digunakan untuk menyelesaikan persamaan diferensial biasa ataupun persamaan diferensial parsial linier dan nonlinier. Metode transformasi diferensial merupakan metode yang menggunakan teori ekspansi deret pangkat pada bentuk transformasinya untuk menentukan solusi. Pada penelitian ini digunakan dua nilai awal pada persamaan Schrodinger yang diberikan. Solusi dengan kedua nilai awal yang diberikan diperoleh dengan menggunakan ekspansi deret Maclaurin. Kemudian solusi tersebut disimulasikan menggunakan software Maple18. Akibatnya, metode transformasi diferensial pada penelitian ini merupakan salah satu metode yang mampu menghasilkan solusi untuk persamaan Schrodinger..Kata Kunci: Persamaan Schrodinger, Metode Transformasi DiferensialAbstract. This study discusses the solution of linear partial differential equations, namely Schrodinger equation. The solution of the equation is done by using the differential transformation method which is a semi-numerical-analytical method, it can be used to solve both ordinary differential equations and linear or nonlinear partial differential equations. Differential transformation method is a method uses the theory of rank expansion in the form of transformation to determine solutions. In this study, two initial values in the given Schrodinger equation were used. Solutions with both initial values given are obtained using the Maclaurin series expansion. Then, the solution is simulated using Maple18 software. As a result, the differential transformation method in this study is one method that is able to solve a solution to the Schrodinger equation.Keywords: Schrodinger Equation, Differential Transformation Method

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