scholarly journals Variation of Parameters for Causal Operator Differential Equations

2017 ◽  
Vol 08 (12) ◽  
pp. 1883-1902
Author(s):  
Reza R. Ahangar
Keyword(s):  
Differential Equations ◽  
Causal Operator ◽  
Variation Of Parameters

Chaotic Dynamics and Bifurcations in Impact Systems

2012 ◽  
Vol 1 (4) ◽  
pp. 15-37
Author(s):  
Sergey Kryzhevich
Keyword(s):  
Periodic Solution ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Chaotic Dynamics ◽  
Invariant Set ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Impact Condition ◽  
Variation Of Parameters

Bifurcations of dynamical systems described byseveral second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to the occurrence of a hyperbolic chaotic invariant set.

Variation of Parameters Method for Solving System of Nonlinear Volterra Integro-Differential Equations

2012 ◽  
Vol 4 (2) ◽  
pp. 190-204
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Asif Waheed ◽  
Eisa Al-Said
Keyword(s):  
Differential Equations ◽  
Vital Role ◽  
Physical Processes ◽  
Variation Of Parameters ◽  
Adomian’S Polynomials

AbstractIt is well known that nonlinear integro-differential equations play vital role in modeling of many physical processes, such as nano-hydrodynamics, drop wise condensation, oceanography, earthquake and wind ripple in desert. Inspired and motivated by these facts, we use the variation of parameters method for solving system of nonlinear Volterra integro-differential equations. The proposed technique is applied without any discretization, perturbation, transformation, restrictive assumptions and is free from Adomian’s polynomials. Several examples are given to verify the reliability and efficiency of the proposed technique.

scholarly journals Researches in physical astronomy

1837 ◽  
Vol 3 ◽  
pp. 101-102
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Variation Of Parameters ◽  
First Approximation ◽  
The One ◽  
Equivalent Method

For the solution of mechanical problems, two methods in general present themselves: the one furnished by the variation of parameters, or constants, which complete the integral obtained by the first approximation,—the other furnished by the integration of the differential equations by means of indeterminate coefficients, or some equivalent method. Each of these methods is applicable to the theory of the perturbations of the heavenly bodies, and they lead to expressions which are of course substantially identical, but which do not appear in the same shape except after certain transformations. The object of the author in the present paper is to effect transformations, by which their identity is established, making use of the developments given in his former papers, published in the Philosophical Transactions. The identity of the results obtained by either methods affords a confirmation of the exactness of those expressions.

A study for steady nanofluid flow between parallel plates

2017 ◽  
Vol 34 (8) ◽  
pp. 2514-2527 ◽  
Author(s):  
Syed Tauseef Mohyud-din ◽  
Muhammad Asad Iqbal ◽  
Muhammad Shakeel
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Uniform Magnetic Field ◽  
Design Methodology ◽  
Magnetic Parameter ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Content Type ◽  
Viscosity Parameter ◽  
Variation Of Parameters

Purpose In this paper, the authors study the behavior of heat and mass transfer between parallel plates of a steady nanofluid flow in the presence of a uniform magnetic field. In the model of nanofluids, the essential effect of thermophoresis and Brownian motion has been encompassed. Design/methodology/approach The variation of parameters method has been exploited to solve the differential equations of nanofluid model. The legitimacy of the variation of parameters method has been corroborated by a comparison of foregoing works by many authors on viscous fluid. Findings An analysis of the model is performed for different parameters, namely, viscosity parameter, Brownian parameter, thermophoretic parameter and magnetic parameter. Originality/value The variation of parameters method proves to be very effective in solving nonlinear system of ordinary differential equations which frequently arise in fluid mechanics.

scholarly journals The method of upper, lower solutions and monotone iterative scheme for higher order hyperbolic partial differential equations

1989 ◽  
Vol 47 (1) ◽  
pp. 153-170 ◽  
Author(s):  
Ravi P. Agarwal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Scheme ◽  
Initial Conditions ◽  
Upper And Lower Solutions ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Monotone Iterative ◽  
Variation Of Parameters ◽  
Variation Of Parameters Formula

AbstractUniformly monotone convergent iterative methods for obtaining multiple solutions of (n + m)th order hyperbolic partial differential equations together with initial conditions are discussed. Appropriate partial differential inequalities which connect upper and lower solutions, and variation of parameters formula is developed.

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