Successive approximation method for Fredholm Integral equation example 2

Example 1:- In this method, we replace the unknown function under the integral sign of the Fredholm integral equation of the second kind by any selective real valued function u0(x) , a ≤ x ≤ b. Accordingly, the first approximation u1(x) of the solution u(x),The second approximation of u2(x) of the solution u(x) can be obtained by replacing u0(x).This process can be continued in the same manner to obtain the nth approximation. In other words, the various approximations of the solution u(x) of (140) can be obtained in a recursive scheme.Even though we can select any real valued function for the zeroth approximation u0(x), the most commonly selected functions for u0(x) are 0, 1 or x. At the limit, the solution u(x) is obtained by as mention in video. Solution of Homogeneous Fredholm integral equation of second kind:-    • Homogeneous Fredholm integral Equation   ....…...................................................................... Like. Share. Comment Subscribe Follow me on Instagram :- @kulsankekumar Integral equation playlist:-    • INTEGRAL EQUATION   .....…...................................................................... What is Integral Equation:-    • Introduction to Integral Equation & its types   What is Fredholm integral equation and its kinds:-    • TYPE 1 Fredholm integral equation with exa...   Homogeneous and non homogeneous Integral equation:-    • Linear and Homogeneous Criterion  for Inte...   ...…...................................................................... Other method to Find to solutions 1) Adomian Decomposition method:-    • Example 1 Adomian Decomposition method II ...   2) Modified Decomposition method:-    • Modified Decomposition method Example 1   3) Noise term phenomenon:-    • Noise Term Phenomenon example 1   4) Direct method:-    • Direct method example 1   5) Successive approximation method:-    • Successive approximation method Example 1   .....…...................................................................... It is important to distinguish between the recursive schemes used in the Adomian decomposition method and in the successive approximations method. In the decomposition method, we apply the approach to determine several components of the solution u(x) so that the zeroth component u0(x) is defined by all terms that are out of the integral sign or part of these terms if the modified version is used. However, in the successive approximations method, we apply the above recursive scheme (143) to determine various approximations of the solution u(x) itself, and not components of u(x). Further, we should note here that the zeroth approximation u0(x) is not defined but rather given by a selective function, and as a result the solution u(x) is given by the formula (144). The successive approximations method will be illustrated by the following examples. #integralequation #integral_equation #Thesuccessiveapproximationmethod #sucessiveapproximationmethod #approximationmethod #solutionofintegralequation #solutionoffresholmintegralequation #mscmaths #mscmathematics #bscmathematics #bscmaths #bsc #msc #exampleoffreddhom #adomiandecompostionmethod #modifieddecompostionmethod #noisetermphenomeon #kthm #solvefredholmintegralequation #introductiontointegralequation solve Integral equation imp examples of successive approximation method important question of successive approximation method solve Integral equation of second kind How to solve the integral equation by successive approximation method What is the successive approximation method solve Fredholm integral Equation solve non Homogeneous Fredholm integral Equation find the solution of Integral equation find solutions of Integral equation of second kind find the solution of non Homogeneous Fredholm integral Equation of second kind find the solution of non Homogeneous integral Equation what is direct method how to find the solution of Fredholm integral Equation using direct method example on direct method example on Fredholm integral Equation example on Integral equation introduction to integral equation methods to find the solution of integral equation