International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.177 Volume 7 Issue XII, Dec 2019- Available at www.ijraset.com © IJRASET: All Rights are Reserved 88 Interpolation Concept in Numerical Computations Vishal Vaman Mehtre 1 , Prem Rajendra Vaidya 2 1 Assistant professor, 2 Student, Department of Electrical Engineering, Bharati Vidyapeeth Deemed To Be University College of Engineering, Pune, India Abstract: In this paper we studied the different types of method used for interpolation. We concluded that all methods used for interpolation depends on certain conditions. I. INTRODUCTION “Interpolation is the process of deriving simple function or data from the discrete data .it can be used to estimate the data of given points. As science and engineering has to deal or work with the discrete data. Interpolation helps to deal with discrete data as it simplify the given complicated discrete data into simple functions. Polynomials are simpler to evaluate, differentiate, integrate, hence they are used for this method and they are called as polynomial interpolation. [3] It can be proven that given n+1 data points it is always possible to find a polynomial of order/degree n to pass through/reproduce the n+ 1 point II. METHODS CAN BE USED FOR INTERPOLATION A. Forward Difference Operator. It is techniques of finding our estimating the value of given function or table from any value. Extrapolation is the process of computing value outside the range. The differences x1 – x0, x2 – x1, x3 – x2, ……, xn – xn–1 when denoted by ey0, ey1, ey2, ……, eyn–1 are respectively, called the first forward differences. {2} B. Backwards Difference Operator. This interpolating technique is used to find the value of the function g = f (x) near the end of table of values, and to extrapolate value of the function a short distance forward from g n , Newton’s backward interpolation.[2] 1) Numericals Based on Above Methods. Q1.calculate forward difference & prepare Forward difference table for following data. X 1 11 21 31 41 51 61 y 19.96 39.65 58.81 77.21 94.61 114.67 125.31 X Y ∆y ∆^2y ∆^3y ∆^4y ∆^5y ∆^6y 1 19.96 19.69 11 39.65 -0.53 19.16 -0.23 21 58.81 -0.76 -0.01 18.4 -0.24 3.91 31 77.21 -1.00 3.90 -23.55 17.4 3.66 -19.6 41 94.61 2.66 -15.74 20.06 -12.08 51 114.67 -9.42 10.64 61 125.31