scholarly journals On Fuzzy differential equation

2019 ◽  
Vol 11 (2) ◽  
pp. 1-9
Author(s):  
Eman Ali Hussain ◽  
Yahya Mourad Abdul – Abbass
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Exact Solutions ◽  
Turing Machine ◽  
Hybrid Method ◽  
Hybrid Methods ◽  
Fitness Function ◽  
Approximate Solutions ◽  
Fuzzy Differential Equation

In this paper, we introduce a hybrid method to use fuzzy differential equation, and Genetic Turing Machine developed for solving nth order fuzzy differential equation under Seikkala differentiability concept [14]. The Errors between the exact solutions and the approximate solutions were computed by fitness function and the Genetic Turing Machine results are obtained. After comparing the approximate solution obtained by the GTM method with approximate to the exact solution, the approximate results by Genetic Turing Machine demonstrate the efficiency of hybrid methods for solving fuzzy differential equations (FDE).

scholarly journals The Laplace-Adomian-Pade Technique for the ENSO Model

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yi Zeng
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
Decomposition Methods ◽  
High Accuracy ◽  
Padé Method

The Laplace-Adomian-Pade method is used to find approximate solutions of differential equations with initial conditions. The oscillation model of the ENSO is an important nonlinear differential equation which is solved analytically in this study. Compared with the exact solution from other decomposition methods, the approximate solution shows the method’s high accuracy with symbolic computation.

scholarly journals Optimal Parameters for Nonlinear Hirota-Satsuma Coupled KdV System by Using Hybrid Firefly Algorithm with Modified Adomian Decomposition

2020 ◽  
Vol 52 (3) ◽  
pp. 339-352
Author(s):  
Omar Saber Qasim ◽  
Karam Adel Abed ◽  
Ahmed F. Qasim
Keyword(s):  
Exact Solutions ◽  
Hybrid Method ◽  
Decomposition Method ◽  
Firefly Algorithm ◽  
Fitness Function ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Optimal Parameters ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper, several parameters of the non-linear Hirota-Satsuma coupled KdV system were estimated using a hybrid between the Firefly Algorithm (FFA) and the Modified Adomian decomposition method (MADM). It turns out that optimal parameters can significantly improve the solutions when using a suitably selected fitness function for this problem. The results obtained show that the approximate solutions are highly compatible with the exact solutions and that the hybrid method FFA_MADM gives higher efficiency and accuracy compared to the classic MADM method.

scholarly journals A solution method for integro-differential equations of conformable fractional derivative

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 7-14 ◽  
Author(s):  
Mustafa Bayram ◽  
Veysel Hatipoglu ◽  
Sertan Alkan ◽  
Sebahat Das
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Fractional Derivatives ◽  
Solution Method ◽  
Approximate Solutions ◽  
Conformable Fractional Derivative ◽  
Conformable Derivative ◽  
Numerical Examples

The aim of this work is to determine an approximate solution of a fractional order Volterra-Fredholm integro-differential equation using by the Sinc-collocation method. Conformable derivative is considered for the fractional derivatives. Some numerical examples having exact solutions are approximately solved. The comparisons of the exact and the approximate solutions of the examples are presented both in tables and graphical forms.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Sinc-Galerkin method for solving hyperbolic partial differential equations

2018 ◽  
Vol 8 (2) ◽  
pp. 250-258 ◽  
Author(s):  
Aydin Secer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Galerkin Method ◽  
Hyperbolic Equations ◽  
Approximate Solutions ◽  
Equation System ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Numerical Examples

In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically.

scholarly journals Existence and uniqueness theorem for a solution of fuzzy differential equations

1999 ◽  
Vol 22 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Jong Yeoul Park ◽  
Hyo Keun Han
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Fuzzy Differential Equation ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of A Solution

By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equationx′(t)=f(t,x(t)),x(t0)=x0. We also consider anϵ-approximate solution of the above fuzzy differential equation.

Bilateral set-valued stochastic integral equations

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3253-3274
Author(s):  
Marek Malinowski ◽  
Donal O'Regan
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Stochastic Integral ◽  
Approximate Solutions ◽  
Existence And Uniqueness Theorem ◽  
Initial State ◽  
Stochastic Integral Equations ◽  
Stability Of The Solution

We investigate bilateral set-valued stochastic integral equations and these equations combine widening and narrrowing set-valued stochastic integral equations studied in literature. An existence and uniqueness theorem is established using approximate solutions. In addition stability of the solution with respect to small changes of the initial state and coefficients is established, also we provide a result on boundedness of the solution, and an estimate on a distance between the exact solution and the approximate solution is given. Finally some implications for deterministic set-valued integral equations are presented.

Time-of-flight diffraction method for joint with linear misalignment

2021 ◽  
Vol 63 (11) ◽  
pp. 654-658
Author(s):  
Y Kurokawa ◽  
T Kawaguchi ◽  
H Inoue
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Geometric Model ◽  
Time Of Flight ◽  
Diffraction Method ◽  
Approximate Solutions ◽  
Weld Joints ◽  
Time Of Flight Diffraction ◽  
Flaw Sizing ◽  
Probe Spacing

The time-of-flight diffraction (TOFD) method is known as one of the most accurate flaw sizing methods among the various ultrasonic testing techniques. However, the standard TOFD method cannot be applied to weld joints with linear misalignment because of its basic assumptions. In this study, a geometric model of the TOFD method for weld joints with linear misalignment is introduced and an exact solution for calculating the flaw tip depth is derived. Since the exact solution is extremely complex, a simple approximate solution is also derived assuming that the misalignment is sufficiently small relative to the probe spacing and the flaw tip depth. The error in the approximate solution is confirmed to be negligible if the assumptions are satisfied. Numerical simulations are conducted to assess the flaw sizing accuracy of both the exact and approximate solutions considering the constraint of the probe spacing and the influence of the excess metal shape. Finally, experiments are conducted to prove the applicability of the proposed method. As a result, the proposed method is proven to enable accurate flaw sizing of weld joints with linear misalignment.

The First Solutions and the Challenge of Their Interpretation

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Gravitational Field ◽  
Exact Solutions ◽  
De Sitter ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Nonlinear Character ◽  
Georges Lemaître

This chapter discusses the first wave of the exploration of exact solutions to Einstein's gravitational field equations. When Einstein published the final form of the field equations in 1915, only an approximate solution was known. Given the complicated nonlinear character of the field equations, he did not expect that exact solutions could easily be found. He was all the more surprised when the astronomer Karl Schwarzschild presented him with just such an exact solution. Thus, this chapter presents a series of these solutions, beginning with the work of Karl Schwarzschild, Johannes Droste, Willem de Sitter, Alexander Friedmann, Hans Reissner, Gunnar Nordström, and finally, Georges Lemaître.

PSEUDODIFFERENTIAL EQUATIONS ON THE SPHERE WITH SPHERICAL SPLINES

2011 ◽  
Vol 21 (09) ◽  
pp. 1933-1959 ◽  
Author(s):  
T. D. PHAM ◽  
T. TRAN ◽  
A. CHERNOV
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Theoretical Result ◽  
Galerkin Method ◽  
Unit Sphere ◽  
Approximate Solutions ◽  
Numerical Results ◽  
Pseudodifferential Equations ◽  
Optimal Convergence ◽  
Sobolev Norms

Spherical splines are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by using Galerkin method. We prove optimal convergence (in Sobolev norms) of the approximate solution by spherical splines to the exact solution. Our numerical results underlie the theoretical result.

Sign in / Sign up

Export Citation Format

Share Document