scholarly journals Solving the Vibrating Spring Equation Using Fuzzy Elzaki Transform

2020 ◽  
Vol 7 (4) ◽  
pp. 549-555
Author(s):  
Rehab Ali Khudair ◽  
Ameera N. Alkiffai ◽  
Athraa Neamah Albukhuttar
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Computational Power ◽  
Fuzzy Transform ◽  
Generalized Differentiability ◽  
Constant Coefficients ◽  
Physical Fields ◽  
New Formula

In this article, a fuzzy Elzaki transform (FZT) is discussed in the context of highly-generalized differentiability concepts, where a new formula of fuzzy derivatives for the fuzzy Elzaki transform is derived as well. It shows the applicability of this interesting fuzzy transform for solving differential equations with constant coefficients also for its computational power. Since ordinary linear equations are mostly used in physical fields, the motion of a mass on a vibrating spring problem is solved by using this kind of fuzzy Elzaki transform.

scholarly journals Using T˜-Transformation for Solving Tank and Heating System Equations

2021 ◽  
Vol 8 (3) ◽  
pp. 441-446
Author(s):  
Rehab A. Khudair ◽  
Ameera N. Alkiffai ◽  
Ahmed S. Sleibi
Keyword(s):  
Differential Equations ◽  
Real Life ◽  
Heating System ◽  
Computational Power ◽  
Fuzzy Transform ◽  
Constant Coefficients ◽  
System Equations ◽  
Fractional Differential ◽  
System Information ◽  
A New Technique

In this article, a fuzzy Tarig evolve (T-n-transform) is implemented. Similar theorems and properties have been proven. To explain the technique of this fuzzy transform in differential equations, examples in real life are presented. This study shows the applicability of this interesting fuzzy transform for solving differential equations with constant coefficients also for its computational power. It is desirable to use it as a new technique, to not only solve “nonlinear fractional differential equations", and to analyze prelocal system information. Moreover, significant theorems are presented to explain the properties of T˜-transform as well as a suggested method is validated with two reality examples.

On a Numerical Method for Solution of the Mathieu-Hill Type Equations

1980 ◽  
Vol 102 (3) ◽  
pp. 619-626 ◽  
Author(s):  
A. Midha ◽  
M. L. Badlani
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Initial Conditions ◽  
Linear Equations ◽  
Solution Process ◽  
Constraint Equations ◽  
Step Functions ◽  
The Matrix ◽  
Constant Coefficients ◽  
Simultaneous Linear Equations

This paper presents a computer-programmable numerical method for the solution of a class of linear, second order differential equations with periodic coefficients of the Mathieu-Hill type. The method is applicable only when the initial conditions are prescribed and the solution is not requiried to be periodic. The solution is facilitated by representing the coefficient functions as a sum of step functions over corresponding sub-intervals of the fundamental interval. During each sub-interval, the solution form is assumed to be that of the differential equations with “constant” coefficients. Constraint equations are derived from imposing the conditions of “compatibility” of response at the end nodes of the intermediate sub-intervals. This set of simultaneous linear equations is expressed in matrix form. The matrix of coefficients may be represented as a triangular one. This form greatly simplifies the solution process for simultaneous equations. The method is illustrated by its application to some specific problems.

scholarly journals Fuzzy Sumudu Transform for Solving System of Linear Fuzzy Differential Equations with Fuzzy Constant Coefficients

2018 ◽  
Author(s):  
Norazrizal Aswad Abdul Rahman ◽  
Muhammad Zaini Ahmad
Keyword(s):  
Differential Equations ◽  
Radioactive Decay ◽  
Research Directions ◽  
Generalized Differentiability ◽  
Numerical Example ◽  
Sumudu Transform ◽  
Constant Coefficients ◽  
Strongly Generalized Differentiability ◽  
Linear Fuzzy Differential Equations ◽  
New Procedures

In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

scholarly journals Comparison theorems for fourth order differential equations

1986 ◽  
Vol 9 (1) ◽  
pp. 105-109
Author(s):  
Garret J. Etgen ◽  
Willie E. Taylor
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Linear Equations ◽  
Oscillation Criterion ◽  
Comparison Theorems ◽  
Positive Continuous Function ◽  
Order Linear ◽  
All Solutions

This paper establishes an apparently overlooked relationship between the pair of fourth order linear equationsyiv−p(x)y=0andyiv+p(x)y=0, wherepis a positive, continuous function defined on[0,∞). It is shown that if all solutions of the first equation are nonoscillatory, then all solutions of the second equation must be nonoscillatory as well. An oscillation criterion for these equations is also given.

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

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