Homogeneous Fredholm integral Equation

Here we find the solution of Homogeneous Fredholm Integral Equation if second kind ....…...................................................................... 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 computation method:-    • Direct method example 1   5) Successive approximation method:-    • Successive approximation method Example 1   .....…...................................................................... In this section we will study the homogeneous Fredholm integral equation with separable kernel given by obtained from (1) by setting f(x) = 0. It is easily seen that the trivial solution u(x) = 0 is a solution of the homogeneous Fredholm integral equation (208). In this study our goal will be focused on finding nontrivial solutions to (208) if exist. We can achieve our goal by introducing the technique that will enable us to determine the nontrivial solutions to (208). Generally speaking, the homogeneous Fredholm integral equation with separable kernel may have nontrivial solutions. Our approach in obtaining these desired solutions will be based mainly on the direct computation method that was employed effectively for nonhomogeneous Fredholm integral equations. We point out that Adomian decomposition method is not applicable for the homogeneous Fredholm integral equations. This may be related to the fact that the nonhomogeneous part f(x) does not exist in this type of problems, and therefore the zeroth component u0(x) cannot be defined. We recall that the direct computation method reduces the equation to an algebraic equation if the kernel consists of one term only, or to a system of algebraic equations if the kernel contains many separable terms. Additional discussions will be required for determining possible values of λ that will give rise to the nontrivial solutions as will be discussed soon. Without loss of generality we may assume a one term kernel given by #integralequation #integral_equation #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 #integralequation #fredholmintegralequation