In this work, we have been found explicit exact soliton wave solutions for Zeldovich
equation with time-dependent coefficients, by using the tanh function method with
nonlinear wave transform, in general case. The results obtained shows that these
exact
solutions are affected the nonlinear nature of the wave variable, it is also shown that this
method is effective and appropriate for solving this kind of nonlinear PDEs, which are
models of many applied problems in physics, chemistry and population evolution.
In this paper, spline technique with five collocation parameters for finding the
numerical solutions of delay differential equations (DDEs) is introduced. The presented
method is based on the approximating the exact solution by C4-Hermite spline
i
nterpolation and as well as five collocation points at every subinterval of DDE.The study
shows that the spline solution of purposed technique is existent and unique and has
strongly stable for some collocation parameters. Moreover, this method if applied to test
problem will be consistent, p-stable and convergent from order nine .In addition ,it
possesses unbounded region of p-stability. Numerical experiments for four examples are
given to verify the reliability and efficiency of the purposed technique. Comparisons show
that numerical results of our method are more accurate than other methods.
In this article, we propose a powerful method called
homotopy perturbation method (HPM) for obtaining the
analytical solutions for an non-linear system of partial
differential equations. We begin this article by apply HPM
method for an important models of linear and non-linear
partial differential equations.
In this paper, we find distributional solutions of boundary value
problems in Sobolev spaces. This solution will be given as Fourier
series with respect to the Eigen functions of a positive definite
operator and its square roots.
Then, we obtain solutions of such problems of a real order.
In this paper, spline approximations with five collocation points are used for the
numerical simulation of stochastic of differential equations(SDE). First, we have modeled
continuous-valued discrete wiener process, and then numerical asymptotic st
ochastic
stability of spline method is studied when applied to SDEs. The study shows that the
method when applied to linear and nonlinear SDEs are stable and convergent.
Moreover, the scheme is tested on two linear and nonlinear problems to illustrate
the applicability and efficiency of the purposed method. Comparisons of our results with
Euler–Maruyama method, Milstein’s method and Runge-Kutta method, it reveals that the
our scheme is better than others.
In this paper we used Liapunov’s Second Method for study of
stability of differential equations system with delay.
This research studies the distributive solutions for some partial
differential equations of second order.
We study specially the distributive solutions for Laplas equation,
Heat equation, wave equations and schrodinger equation.
We introduce the
fundamental solutions for precedent equations
and inference the distributive solutions by using the convolution of
distributions concept. For that we use some of lemmas and theorems
with proofs, specially for Laplas equation. And precedent some of
concepts, defintions and remarks.
المعادلة التفاضلية الجزئية من المرتبة الثانية
التوزيعات
الجداء التنسوري للتوزبعات
التفاف التوزيعات
الحلول الأساسية
الحلول التوزيعية
partial differential equations of second order
Distributions
Tensor product of distributions
Convolution of distributions
Fundamental solution
Distributive solution
المزيد..
In this work, we have found exact traveling wave solutions for generalized Fitzhug-
Nagumo equation with arbitrary constant coefficients, by using the homogeneous balance
method, The obtained results shows that these solutions changes with the spec
ials solution
of Ricati ODE with arbitrary constant coefficients , and shows that this method is simple,
direct and very efficient for solving this kind of nonlinear PDEs, It can be applied to
nonlinear PDEs which frequently arise in engineering sciences, mathematical physics and
other scientific real-time applications fields.
This work suggests a study of small motions of system of anideal-relaxing fluids which rotate ina limited space. First, we present the problem and reducethe initial boundary value problem that describe it to Cauchy problem for an ordinary differentia
l equation of the second order form in Hilbert space. This allows us to prove the unique solvability theorem.
The goal of this work is finding exact solitary wave solutions to generalized Fitzhug-Nagumo equation with constant coefficients, by using the exp-function method, where we have illustrated graphically one of them, the obtained results, with aid of s
ymbolic programs as Maple and Mathematica, show that this method is simple, direct and very efficient for solving this kind of nonlinear PDEs, and it requires no advanced mathematical knowledge, so it is convenient to scientists and engineering.
