In this paper we introduce a new method for solving partial and ordinary differential equations with large first, second and third derivatives of the solution in some part of the domain using the finite element technique (here called the Galerkin-Gokhman method). The method is based on the application of the Galerkin method to a modified differential equation. The exact solution of the modified...

in this paper, we intend to solve special kind of ordinary differential equations which is called heun equations, by converting to a corresponding stochastic differential equation(s.d.e.). so, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this s.d.e. is solved by numerically methods. mo...

3 4 CONTENTS Preface These lecture notes are intented as an introduction to linear second order elliptic partial differential equations. It can be considered as a continuation of a chapter on elliptic equations of the lecture notes [17] on partial differential equations. In [17] we focused our attention mainly on explicit solutions for standard problems for elliptic, parabolic and hyperbolic eq...

  Normal 0 false false false ...

1. The stationary, irrotational flow of a compressible fluid is characterized by a quasi-linear second order partial differential equation with coefficients which are functions of the first derivatives. The equation is sometimes elliptic and sometimes hyperbolic, depending on the magnitude of these first derivatives. The question of the existence of such flows satisfying prescribed conditions i...

where E(x, y) > 0. The parametric curves x = const. and y = const. form an isothermal net on 1. It is well known that h(x, y) = c, where h is a harmonic function of (x, y), that is, h satisfies the Laplace equation, hA, + h,, = 0, defines an isothermal family of curves on Z. The constant c is called the isothermal parameter. The converse of the preceding statement is not valid. That is, if g(x,...

in this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an ivp of first order hybrid  random differential equations with the linear perturbation of second type. a comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential equ...

Introduction. The purpose of this paper is to describe an effective construction of Greene and Neumann's functions for a general class of linear, second-order partial differential equations of elliptic type in terms of a set of continuously differentiable functions, complete and orthonormal with respect to the domain considered. This result completes a previous paper by us in which an analogous...