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

scholarly journals Wave Structures for Nonlinear Schrodinger Types Fractional Partial Differential Equations Arise in Physical Sciences

2021 ◽  
Vol 9 (2) ◽  
pp. 101-110
Author(s):  
Mst. Nasrin Nahar ◽  
Md. Tarikul Islam ◽  
Diganta Broto Kar
Keyword(s):  
Partial Differential Equations ◽  
Schrödinger Equation ◽  
Differential Equations ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Nonlinear Phenomena ◽  
Partial Differential ◽  
Nonlinear Schrödinger

Nonlinear partial differential equations are mostly renowned for depicting the underlying behavior of nonlinear phenomena relating to the nature of the real world. In this paper, we discuss analytic solutions of fractional-order nonlinear Schrodinger types equations such as the space-time fractional nonlinear Schrodinger equation and the (2+1)-dimensional time-fractional Schrodinger equation. The considered equations are converted into ordinary differential equations with the help of wave variable transformation and then the recently established rational ( )-expansion method is employed to construct the exact solutions. The obtained solutions have appeared in the forms of a trigonometric function, hyperbolic function, and rational function which are compared with those of literature and claimed to be different. The graphical representations of the solutions are finally brought out for their physical appearances. The applied method is seemed to be efficient, concise, and productive which might be used for further research. Mathematics Subject Classifications: 35C08, 35R11

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.

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