scholarly journals Piecewise Analytic Method (PAM) is a New Step in the Evolution of Solving Nonlinear Differential Equation

2019 ◽  
Vol 8 (1) ◽  
pp. 12
Author(s):  
Tamer Abassy
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
New Method ◽  
Analytic Method ◽  
Highly Nonlinear

In this paper, a new method is introduced for engineers and scientists which can be used for solving highly nonlinear differential equations. The method is called Piecewise Analytic Method (PAM). PAM is used to solve problems which other methods can't solve. The paper also shows how the accuracy and error can be controlled according to the needs.

scholarly journals ANALYTICAL TECHNIQUE WITH LAGRANGE MULTIPLIER FOR SOLVING SPECIFIC NONLINEAR DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 21 (1) ◽  
pp. 5-14
Author(s):  
NAWAB KHAN ◽  
QAZI MAHMOOD UL HASSAN ◽  
EHSAN UL HAQ ◽  
M. YAQUB KHAN ◽  
KAMRAN AYUB ◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Lagrange Multiplier ◽  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
New Method ◽  
Numerical Examples ◽  
Analytical Technique

This paper will use Lagrange parameter in Adomain decomposition method to suggest new method for solving nonlinear differential equation. This method will be highly order convergent. Also, this method will be compared with old existence method. At last, some numerical examples will be given to illustrate the efficiency of newly developed method.

scholarly journals Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Kun-Wen Wen ◽  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Third Order ◽  
Order Nonlinear Differential Equation ◽  
Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

scholarly journals On the asymptotic behavior of solutions of certain third-order nonlinear differential equations

2005 ◽  
Vol 2005 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
The Third ◽  
All Solutions

We establish sufficient conditions under which all solutions of the third-order nonlinear differential equation x ⃛+ψ(x,x˙,x¨)x¨+f(x,x˙)=p(t,x,x˙,x¨) are bounded and converge to zero as t→∞.

Oscillation of Second-Order Nonlinear Differential Equations

2014 ◽  
Vol 548-549 ◽  
pp. 1007-1010
Author(s):  
Qing Zhu ◽  
Zhi Bin Ma
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Order Nonlinear Differential Equation

A new oscillation criterion is established for a certain class of second-order nonlinear differential equation x"(t)-b(t)x'(t)+c(t)g(x)=0, x"(t)+c(t)g(x)=0 that is different from most known ones. Some applications of the result obtained are also presented. Our results are sharper than some previous ones.

scholarly journals On the correct formulation of a nonlinear differential equations in Banach space

2001 ◽  
Vol 26 (7) ◽  
pp. 437-444
Author(s):  
Mahmoud M. El-Borai ◽  
Osama L. Moustafa ◽  
Fayez H. Michael
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Nonlinear Differential Equations ◽  
Initial Value ◽  
Correct Formulation

We study, the existence and uniqueness of the initial value problems in a Banach spaceEfor the abstract nonlinear differential equation(dn−1/dtn−1)(du/dt+Au)=B(t)u+f(t,W(t)), and consider the correct solution of this problem. We also give an application of the theory of partial differential equations.

scholarly journals Oscillation and nonoscillation theorems for second order nonlinear differential equations

2001 ◽  
Vol 32 (2) ◽  
pp. 95-102
Author(s):  
Jiang Jianchu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Order Nonlinear Differential Equation ◽  
Oscillation And Nonoscillation

New oscillation and nonoscillation theorems are obtained for the second order nonlinear differential equation $$ (|u'(t)|^{\alpha -1} u'(t))' + p(t)|u(t)|^{\alpha -1} u(t) = 0 $$ where $ p(t) \in C [0, \infty) $ and $ p(t) \ge 0 $. Conditions only about the integrals of $ p(t) $ on every interval $ [2^n t_0, 2^{n+1} t_0] $ ($ n = 1, 2, \ldots $) for some fixed $ t_0 >0 $ are used in the results.

Oscillation Criteria for Second Order Nonlinear Differential Equations Involving Integral Averages

1993 ◽  
Vol 45 (5) ◽  
pp. 1094-1103 ◽  
Author(s):  
James S. W. Wong
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Equation ◽  
Nonlinear Differential Equation ◽  
General Equation ◽  
Nonlinear Differential Equations ◽  
Nonlinear Function ◽  
Second Order ◽  
Oscillation Criteria ◽  
Fowler Equation

AbstractConsider the second order nonlinear differential equationy" + a(t)f(y) = 0where a(t) ∈ C[0,∞),f(y) GC1 (-∞, ∞),ƒ'(y) ≥ 0 and yf(y) > 0 for y ≠ 0. Furthermore, f(y) also satisfies either a superlinear or a sublinear condition, which covers the prototype nonlinear function f(y) = |γ|γ sgny with γ > 1 and 0 < γ < 1 known as the Emden-Fowler case. The coefficient a(t) is allowed to be negative for arbitrarily large values of t. Oscillation criteria involving integral averages of a(t) due to Wintner, Hartman, and recently Butler, Erbe and Mingarelli for the linear equation are shown to remain valid for the general equation, subject to certain nonlinear conditions on f(y). In particular, these results are therefore valid for the Emden-Fowler equation.

scholarly journals On the Generalized Simplest Equations: Toward the Solution of Nonlinear Differential Equations with Variable Coefficients

2021 ◽  
Author(s):  
Gunawan Nugroho ◽  
Purwadi Agus Darwito ◽  
Ruri Agung Wahyuono ◽  
Murry Raditya
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Riccati Equation ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Variable Coefficients ◽  
Higher Order ◽  
First Order ◽  
Generalized Riccati Equation ◽  
Polynomial Differential Equation

The simplest equations with variable coefficients are considered in this research. The purpose of this study is to extend the procedure for solving the nonlinear differential equation with variable coefficients. In this case, the generalized Riccati equation is solved and becomes a basis to tackle the nonlinear differential equations with variable coefficients. The method shows that Jacobi and Weierstrass equations can be rearranged to become Riccati equation. It is also important to highlight that the solving procedure also involves the reduction of higher order polynomials with examples of Korteweg de Vries and elliptic-like equations. The generalization of the method is also explained for the case of first order polynomial differential equation.

scholarly journals Asymptotic linearity of solutions of nonlinear differential equations

1987 ◽  
Vol 35 (2) ◽  
pp. 257-265 ◽  
Author(s):  
Shaozhu Chen
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Necessary Conditions ◽  
Nonlinear Differential Equations ◽  
Asymptotic Linearity

In this paper we establish sufficient or necessary conditions for the nonlinear differential equation u″ + f (t, u) = 0 to have solutions which are asymptotic to lines with non-zero slopes and correct some formulations in theorems obtained by D.S. Cohen and J. Tong.

scholarly journals Existence for Nonoscillatory Solutions of Higher-Order Nonlinear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Yazhou Tian ◽  
Fanwei Meng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Higher Order ◽  
Nonoscillatory Solutions ◽  
Order Nonlinear Differential Equation

The existence of nonoscillatory solutions of the higher-order nonlinear differential equation [r(t)(x(t)+P(t)x(t-τ))(n-1)]′+∑i=1mQi(t)fi(x(t-σi))=0,  t≥t0, where m≥1,n≥2 are integers, τ>0,  σi≥0,  r,P,Qi∈C([t0,∞),R),  fi∈C(R,R)  (i=1,2,…,m), is studied. Some new sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for general Qi(t)  (i=1,2,…,m) which means that we allow oscillatory Qi(t)  (i=1,2,…,m). In particular, our results improve essentially and extend some known results in the recent references.

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