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Register a new userProgramming Solutions for Some Nonlinear Partial Differential Equations
حلول برمجية لبعض المعادلات التفاضلية الجزئية غير الخطية
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Damascus University أطروحة دكتوراه
Publication date
2018
fields
Mathematics
and research's language is
العربية
Created by
Shamra Editor
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قدمنا في هذا العمل حلولا برمجية لمجموعة من المعادلات التفاضلية الجزئية غير الخطية هي معادلة الحمل غير الخطية وغير المتجانسة، وصف معادلات KdV من المرتبة الثالثة وصف معادلات Burgers.
In this work, we present programming solutions for some nonlinear partial differential equations, which are the advection equation, the third-order KdV equations, and a family of Burgers' equations.
References used
Ablowitz M.J and Clarkson P.A. Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, 1991.
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In this article, powerful approximate analytical
methods, called Adomian decomposition method and
variational iteration method are introduced and applied to
obtaining the approximate analytical solutions for an
important models of linear and non-
linear partial differential
equations such as ( nonlinear Klein Gordon equation -
nonlinear wave equation - linear telegraph equation -
nonlinear diffusion convection equation ) .
The studied examples are used to reveal that those methods are
very effective and convenient for solving linear and nonlinear
partial differential equations .
Numerical results and comparisons with the exact solution are
included to show validity, ability, accuracy, strength and
effectiveness of those techniques.
معادلة الموجة
wave equation
طريقة تفريق أدوميان
طريقة التكرار التغايري
حدودية أدوميان
معادلة كلاين غوردن
معادلة التلغراف
معادلة الانتشار الحراري
Adomian Decomposition Method
Variational Iteration Method
Adomian Polynomial
Klien Gordon equation
Telegraph equation
Diffusion Convection equation
المزيد..
In this paper, we present two new methods for finding
the numerical solutions of systems of the nonlinear equations.
The basic idea depend on
founding relationship between minimum of a function and the
solution of systems of the nonlinear equatio
ns. The first method
seeks the numerical solution with a sequence of search
directions, which is depended on gradient and Hessian matrix of
function, while the second method is based on a sequence of
conjugate search directions. The study shows that our two
methods are convergent, and they can find exact solutions for
quadratic functions, so they can find high accurate solutions for
over quadratic functions. The purposed two algorithms are
programmed by Mathematica Version9. The approximate
solutions of some test problems are given. Comparisons of our
results with other methods illustrate the efficiency and highly
accurate of our suggested methods.
In this paper, we study the oscillation and nonoscillation theorems
for second order nonlinear difference equations.
By using some important of definitions and main concepts in
oscillation, in addition for lemmas, we introduce examples
illustrating the relevance of the theorems discussed.
In this paper ,we study asymptotic properties of solutions of the following
third – order differential equations with -P Laplacian.
In the sequel,it is assumed that all solutions of the equation are
continuously extendable throughout the entire re
al axis.
We shall prove sufficient conditions under which all global solutions
In this paper, we introduce a numerical method for solving systems of high-index differential algebraic equations. This method is based on approximating the exact solution by spline polynomial of degree eight with five collocation points to find the
numerical solution in each step. The study shows that the method when applied to linear differential-algebraic systems with index equal one is stable and convergent of order 8, while it is stable and convergent of order 9-u for index equal u .
Numerical experiments for four test examples and comparisons with other available results are given to illustrate the applicability and efficiency of the presented method
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