Homogeneous Fredholm integral Equation

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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 i... • What is Fredholm integral equation and its kinds:- • TYPE 1 Fredholm integral equation wit... • Homogeneous and non homogeneous Integral equation:- • Linear and Homogeneous Criterion for... • ...…...................................................................... • Other method to Find to solutions • 1) Adomian Decomposition method:- • Example 1 Adomian Decomposition metho... • 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 Examp... • .....…...................................................................... • 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

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