Modified Decomposition method Example 1

In this Video we shall be concerned with the nonhomogeneous Fredholm integral equations of the second kind . Example 2:-    • Modified Decomposition method example 2   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...   The decomposition method and the modified decomposition method introduce the solution of Fredholm integral equation in the form of a rapidly convergent power series with elegantly computable terms. However, if f(x) consists of more than one term, the modified decomposition method minimizes the volume of the computational work. Previous Video:- Adomian decomposition Method :    • What is Adomian Decomposition method,...   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...   There are so many ways to find the solutions of Non Homogeneous Fredholm integral equation. The following ways are 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 method:-    • Direct method example 1   5) Successive approximation method:-    • Successive approximation method Examp...   LIKE COMMENT SHARE SUBSCRIBE ------------------------------------------------------------- Follow us Insta:-- @kulsanketkumar Integral equation Playlist:-    • INTEGRAL EQUATION   ------------------------------------------------------------------ The Modified Decomposition Method It is worth noting that the Adomian decomposition method may be sometimes implemented in a different but easier manner in order to facilitate the computational work. It is recommended to apply the modified decomposition method, developed by Wazwaz [ 59], for cases where the nonhomogeneous part f(x) in (1) consists of a combination of many terms. This modified technique, as will be seen later, will minimize the volume of calculations and reduce the several integral evaluations that result in applying the standard Adomian decomposition method. It is also of interest, before giving a clear discussion of this method, to note that this modified technique will be carried out with promising results in Volterra integral equations and nonlinear integral equations in forthcoming chapters. The technique avoids the cumbersome integrations of other methods. In the modified method, we split the given function f(x) into two parts defined by where f0(x) consists of number of terms of f(x), and f1(x) includes the remaining terms of f(x). We note that a necessary condition is required to apply this approach in that f(x) should consist of more than one term as shown by (38). In view of (38), the integral equation (1) becomes #integralequation #solutionofintegraequation #modifieddecompositionmethod #nonhomogeneousintegralequation #mscmaths #maths #mathematics #enigneeringmathematics #Fredholm #fredholmintegralequation #fredholm_integral_equation #fredholmintegralequation