• Title, Summary, Keyword: function differential equation

Search Result 299, Processing Time 0.042 seconds

THE PARTIAL DIFFERENTIAL EQUATION ON FUNCTION SPACE WITH RESPECT TO AN INTEGRAL EQUATION

  • Chang, Seung-Jun;Lee, Sang-Deok
    • The Pure and Applied Mathematics
    • /
    • v.4 no.1
    • /
    • pp.47-60
    • /
    • 1997
  • In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.

  • PDF

APPLICATION OF EXP-FUNCTION METHOD FOR A CLASS OF NONLINEAR PDE'S ARISING IN MATHEMATICAL PHYSICS

  • Parand, Kourosh;Amani Rad, Jamal;Rezaei, Alireza
    • Journal of applied mathematics & informatics
    • /
    • v.29 no.3_4
    • /
    • pp.763-779
    • /
    • 2011
  • In this paper we apply the Exp-function method to obtain traveling wave solutions of three nonlinear partial differential equations, namely, generalized sinh-Gordon equation, generalized form of the famous sinh-Gordon equation, and double combined sinh-cosh-Gordon equation. These equations play a very important role in mathematical physics and engineering sciences. The Exp-Function method changes the problem from solving nonlinear partial differential equations to solving a ordinary differential equation. Mainly we try to present an application of Exp-function method taking to consideration rectifying a commonly occurring errors during some of recent works.

ON PERIODICIZING FUNCTIONS

  • Naito Toshiki;Shin Jong-Son
    • Bulletin of the Korean Mathematical Society
    • /
    • v.43 no.2
    • /
    • pp.253-263
    • /
    • 2006
  • In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.

HOMOGENEOUS FUNCTION AND ITS APPLICATION IN A FINSLER SPACE

  • Kim, Byung-Doo;Choi, Eun-Seo
    • Communications of the Korean Mathematical Society
    • /
    • v.14 no.2
    • /
    • pp.385-392
    • /
    • 1999
  • We deal with a differential equation which is constructed from homogeneous function, and its geometrical meaning in a Finsler space. Moreover, were prove that a locally Minkowski space satisfying a differential equation F\ulcorner=0 is flat-parallel.

  • PDF

Physics based basis function for vibration analysis of high speed rotating beams

  • Ganesh, R.;Ganguli, Ranjan
    • Structural Engineering and Mechanics
    • /
    • v.39 no.1
    • /
    • pp.21-46
    • /
    • 2011
  • The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

ON ZEROS AND GROWTH OF SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS

  • Kumar, Sanjay;Saini, Manisha
    • Communications of the Korean Mathematical Society
    • /
    • v.35 no.1
    • /
    • pp.229-241
    • /
    • 2020
  • For a second order linear differential equation f" + A(z)f' + B(z)f = 0, with A(z) and B(z) being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.

Stationary analysis of the surplus process in a risk model with investments

  • Lee, Eui Yong
    • Journal of the Korean Data and Information Science Society
    • /
    • v.25 no.4
    • /
    • pp.915-920
    • /
    • 2014
  • We consider a continuous time surplus process with investments the sizes of which are independent and identically distributed. It is assumed that an investment of the surplus to other business is made, if and only if the surplus reaches a given sufficient level. We establish an integro-differential equation for the distribution function of the surplus and solve the equation to obtain the moment generating function for the stationary distribution of the surplus. As a consequence, we obtain the first and second moments of the level of the surplus in an infinite horizon.

DISCUSSION ON THE ANALYTIC SOLUTIONS OF THE SECOND-ORDER ITERATED DIFFERENTIAL EQUATION

  • Liu, HanZe;Li, WenRong
    • Bulletin of the Korean Mathematical Society
    • /
    • v.43 no.4
    • /
    • pp.791-804
    • /
    • 2006
  • This paper is concerned with a second-order iterated differential equation of the form $c_0x'(Z)+c_1x'(z)+c_2x(z)=x(az+bx(z))+h(z)$ with the distinctive feature that the argument of the unknown function depends on the state. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained.

NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATION CORRESPONDING TO CONTINUOUS DISTRIBUTIONS

  • Amini, Mohammad;Soheili, Ali Reza;Allahdadi, Mahdi
    • Communications of the Korean Mathematical Society
    • /
    • v.26 no.4
    • /
    • pp.709-720
    • /
    • 2011
  • We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.