SOLUTION OF FIRST ORDER DIFFERENTIAL EQUATION USING NUMERICAL NEWTON’S INTERPOLATION AND LAGRANGE

Author (s) : Dr.B.MOHANAPRIYA and Dr.R.PRABHU

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Abstract :
In this paper, A differential equation is then an infinite number of equations, one for each x in the domain. The analytic or exact solution is the functional expression of u or for the example case u(x) = sin(x) + c where c is an arbitrary constant. This can be verified using Maple and the command d solve(diff(u(x),x)=cos(x)); . Because of this non uniqueness which is inherent in differential equations we typically include some additional equations. For our example case, an appropriate additional equation would be u(1) = 2 which would allow us to determine c to be 2 − sin(1) and hence recover the unique analytical solution u(x) = sin(x)+2 − sin(1). Here the appropriate Maple command is d solve(diff(u(x),x)=cos(x),u(1)=2);. The differential equation together with the additional equation(s) are denoted a differential equation problem. Further, this analytic solution must depend continuously on the data in the (vague) sense that if the equations are changed slightly then also the solution does not change too much. The study in this regard wishes to determine the solution of first order differential equation using numerical Newton’s interpolation and Lagrange.

Keywords : Numerical Newton’s interpolation and Lagrange

Conference Date : 30/08/2019

Pages : 166

Paper ID : 19164