EXISTENCE AND UNIQUNESS OF SOLUTION

Author (s) : R.BANU and M.PARIMALA

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Abstract :
In the this paper, we developed methods of finding explicitly the general solutions of non-homogeneous differential equations as a sum of a particular solution and a solution of the homogeneous part of the equation and noted in most of the cases that the solutions are expressible in terms of the well-known special functions. we discussed some second order liner equations whose solutions are not expressible as special functions but they possess analytic solutions in the sense that their solutions are given by different convergent power serious. All through, we did not devise a general method which can assert theoretically the existence and uniqueness of solutions of a wider class of first order differential equations. Discusses in detail the approximation method of Picard to the solution of the initial value problem of the general first order non-liner differential equation of the type   x(t) = f(t.x), x(t) = 1. Where f (t, x) is some arbitrary function defined and continuous in some neighbourhood of (t, x) The Picard's theorem gives the unique solution of the above initial value problem (1) by the method of successive approximations, using the integral equation equivalent to the given non-linear differential equation.

Keywords : Non-linear differential equation, integral equation

Conference Date : 30/08/2019

Pages : 159

Paper ID : 19157