scholarly journals About Exact Solution of Some Non Linear Partial Integro-differential Equations

2021 ◽  
Vol 10 (1) ◽  
pp. 19
Author(s):  
Francis Bassono ◽  
Rasmané Yaro ◽  
Joseph Bonazebi Yindoula ◽  
Gires Dimitri Nkaya ◽  
Gabriel Bissanga
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Non Linear

scholarly journals On a class of non-linear differential equations with exact solution

2012 ◽  
Vol 34 (1) ◽  
pp. 7-17
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Solid Mechanics ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Second Order Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The present paper deals with a class of non-linear ordinary second-order differential equations with exact solutions. A procedure for finding the general exact solution based on a known particular one is derived. For illustration solutions of some non-linear equations occurred in many problems of solid mechanics are considered.

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 A New Improved Adomian Decomposition Method for Solving Emden{Fowler Type Equations of Higher{Order

2020 ◽  
pp. 9-17
Author(s):  
Zainab Ali Abdu AL-Rabahi ◽  
Yahya Qaid Hasan
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Linear Problems ◽  
Suggested Modification

In this paper, we present a suggested modification for Adomain decomposition method to solve Emden{Fowler Types Equations of higher-order ordinary differential equations. The proposed method can be applied to linear and non-linear problems. By using some illustrative examples, we tested the reliability and effectiveness of the proposed method and we found that the obtained results approximate the exact solution. Thus, we can conclude that this proposed method is efficient and reliable .

scholarly journals Numerical Solution of Non-linear Delay Differential Equations Using Semi Analytic Iterative Method

2019 ◽  
Vol 25 (103) ◽  
pp. 131-142
Author(s):  
Asmaa A. Aswhad ◽  
Samaher M. Yassein
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Numerical Solution ◽  
Delay Differential Equations ◽  
Initial Conditions ◽  
Linear Delay ◽  
Non Linear ◽  
Delay Differential

       We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.                       

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

Marine Pipeline Analysis Based on Newton’s Method With an Arctic Application

1970 ◽  
Vol 92 (4) ◽  
pp. 827-833 ◽  
Author(s):  
D. W. Dareing ◽  
R. F. Neathery
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Newton’S Method ◽  
Finite Differences ◽  
Newton's Method ◽  
Nonlinear Differential Equations ◽  
Bending Moments ◽  
Iterative Solutions ◽  
Linear Differential ◽  
Pipe Deflection

Newton’s method is used to solve the nonlinear differential equations of bending for marine pipelines suspended between a lay-barge and the ocean floor. Newton’s method leads to linear differential equations, which are expressed in terms of finite differences and solved numerically. The success of Newton’s method depends on initial trial solutions, which in this paper are catenaries. Iterative solutions converge rapidly toward the exact solution (pipe deflection) even though large bending moments exist in the pipe. Example calculations are given for a 48-in. pipeline suspended in 300 ft of water.

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