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Direct method example 1
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Direct method for fredholm integral equation • special example where two scalers are introduce :- • Direct method special example • 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... • .....…...................................................................... • .....…...................................................................... • Like. Share. Comment Subscribe • Follow me on Instagram :- @kulsankekumar • Integral equation playlist:- • INTEGRAL EQUATION • .....…...................................................................... • Other method to Find to the solutions of Fredholm integral equation • 1) Adomian Decomposition method for FIE:- • Example 1 Adomian Decomposition metho... • 2) Modified Decomposition method for FIE:- • Modified Decomposition method Example 1 • 3) Noise term phenomenon for FIE :- • Noise Term Phenomenon example 1 • 4) Direct method for FIE:- • Direct method example 1 • 5) Successive approximation method for FIE :- • Successive approximation method Examp... • .....…...................................................................... • The Direct Computation Method • We next introduce an efficient traditional method for solving Fredholm integral • equations of the second kind ,called the direct computational method. Recall that our • attention will be focused on separable or degenerate kernels K(x, t) expressed in the • form defined by . Without loss of generality, we may assume that the kernel of • can be expressed as K(x,t) = g(x)h(t) • It is worth noting that the direct computation method determines the exact solution in • a closed form, rather than a series form, provided that the constant α is evaluated. In • addition, this method usually gives rise to a system of algebraic equations depending on • the structure of the kernel, where sometimes we need to evaluate more than one constant • as will be seen in Examples . For linear Fredholm integral equations, we obtain • one value for α, or one value for each of α and β if these two constants are used. This is • due to the fact that linear equation has a unique solution. • In what follows, we examine four illustrative examples by using the direct • computation method. • use the direct computation method to solve the following Fredholm • integral equation • • In closing this section, we point out that the direct computation method introduces a • very direct technique to formally determine the solution of Fredholm integral equation. • In this method, the Fredholm integral equation will be transformed into a more readily • solvable integral. Moreover, the direct computation method introduces the exact • solution in a closed form rather than a series form as in the case of the decomposition • method or the variational iteration method. The other traditional methods, that will be • discussed in the forthcoming sections, also determine the solution in a series form, but • in a different approach than the decomposition method or the variational iteration • method. We remark here that the direct computation method was introduced in this • section in a slightly different manner than other texts. • • • #integralequation • #directmethod • #directcomputationmethod • #solutionofintegralequation • #solutionoffresholmintegralequation • #mscmaths • #mscmathematics • #bscmathematics • #bscmaths • #bsc • #exampleoffreddhom • #adomiandecompostionmethod • #modifieddecompostionmethod • #noisetermphenomeon • #kthm • #solvefredholmintegralequation • #introductiontointegralequation • • solve Integral equation • direct computation method • solve Integral equation of second kind • 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 for fredholm integral equation • example on Fredholm integral Equation • example on Integral equation • introduction to integral equation
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