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 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 Reliable Iterative Method for solving Volterra - Fredholm Integro Differential Equations

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Samaher Marez
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Iterative Process ◽  
Initial Conditions ◽  
High Accuracy ◽  
Series Solutions ◽  
Math Program ◽  
The Right

  The aim of this paper, a reliable iterative method is presented for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method.  Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibit that this technique has compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

scholarly journals On the exact and approximate solutions of several differential equations with variational derivatives of the first and second orders

2020 ◽  
Vol 56 (1) ◽  
pp. 51-71
Author(s):  
M. V. Ignatenko ◽  
L. A. Yanovich
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Approximate Solution ◽  
Differential Equations ◽  
Interpolation Problem ◽  
Approximate Solutions ◽  
Hyperbolic Type ◽  
The Cauchy Problem ◽  
Variational Derivatives ◽  
Derivatives Of

In this paper, we consider the problem of the exact and approximate solutions of certain differential equations with variational derivatives of the first and second orders. Some information about the variational derivatives and explicit formulas for the exact solutions of the simplest equations with the first variational derivatives are given. An interpolation method for solving ordinary differential equations with variational derivatives is demonstrated. The general scheme of an approximate solution of the Cauchy problem for nonlinear differential equations with variational derivatives of the first order, based on the use of the operator interpolation apparatus, is presented. The exact solution of the differential equation of the hyperbolic type with variational derivatives, similar to the classical Dalamber solution, is obtained. The Hermite interpolation problem with the conditions of coincidence in the nodes of the interpolated and interpolation functionals, as well as their variational derivatives of the first and second orders, is considered for functionals defined on the sets of differentiable functions. The found explicit representation of the solution of the given interpolation problem is based on an arbitrary Chebyshev system of functions. This solution is generalized for the case of interpolation of functionals on one out of two variables and applied to construct an approximate solution of the Cauchy problem for the differential equation of the hyperbolic type with variational derivatives. The description of the material is illustrated by numerous examples.

Numerical Solution to Volterra-Type Integro-Differential Equations of the Second Kinds by Legendre Collocation Method

2014 ◽  
Vol 687-691 ◽  
pp. 1522-1527
Author(s):  
Ting Jing Zhao
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Collocation Method ◽  
High Accuracy ◽  
Time Step ◽  
Volterra Type ◽  
Legendre Collocation Method

The purpose of this paper is to propose an efficient numerical method for solving Volterra-type integro-differential equation of the second kinds. This method based on Legendre-Gauss-Radau collocation, which is easy to be implemented especially for nonlinear and possesses high accuracy. Also, the method can be done by proceeding in time step by step. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique, and the results have been compared with the exact solution.

On a class of differential equations which model tide-well systems

1970 ◽  
Vol 3 (3) ◽  
pp. 391-411 ◽  
Author(s):  
B. J. Noye
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Steady State ◽  
Differential Equations ◽  
Sea Level ◽  
Approximate Solutions ◽  
Near Resonance ◽  
Non Linear ◽  
Image Position ◽  
Steady State Solutions

For three possible types of tide-well systems the non-dimensional head response, Y(τ), to a sinusoidal fluctuation of the sea-level is given by the differential equation Estimates of the non-dimensional well response Z(τ) = sinτ - Y(τ) are found by considering the steady state solutions of the above equation. With n = 2 the equation is linear and an exact solution can be found; for n ≠ 2 the equation is non-linear and several methods which give approximate solutions are described. The methods used can be extended to cover other values of n; for example, with n = 4 the equation corresponds to one governing oscillations near resonance in open pipes.

scholarly journals Comparison for the Approximate Solution of the Second-Order Fuzzy Nonlinear Differential Equation with Fuzzy Initial Conditions

2020 ◽  
Vol 8 (5) ◽  
pp. 527-534
Author(s):  
Ali F Jameel ◽  
Akram H. Shather ◽  
N.R. Anakira ◽  
A. K. Alomari ◽  
Azizan Saaban
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Nonlinear Differential Equation ◽  
Initial Conditions ◽  
Second Order

scholarly journals Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Yongjin Li ◽  
Yan Shen
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Linear Differential ◽  
The Stability

The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second ordery′′+p(x)y′+q(x)y+r(x)=0. That is, iffis an approximate solution of the equationy′′+p(x)y′+q(x)y+r(x)=0, then there exists an exact solution of the equation near tof.

scholarly journals Approximate Solutions for Flow with a Stretching Boundary due to Partial Slip

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
U. Filobello-Nino ◽  
H. Vazquez-Leal ◽  
A. Sarmiento-Reyes ◽  
B. Benhammouda ◽  
V. M. Jimenez-Fernandez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Perturbation Method ◽  
Nonlinear Differential Equation ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Accurate Solution ◽  
Partial Slip ◽  
Homotopy Perturbation

The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear differential equation that describes the behaviour of a flow with a stretching flat boundary due to partial slip. Comparing results between approximate and numerical solutions, we concluded that our results are capable of providing an accurate solution and are extremely efficient.

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).

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

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