C - Fen Bilimleri Enstitüsü - Erciyes Üniversitesi

136Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi 26(2): 131-142 (2010)⎡c⎢⎢c⎢⎣c012⎤ ⎡37/27⎥=⎢⎥ ⎢20/27⎥⎦⎢⎣10/275/5422/275/542/27 ⎤ ⎡ 1.8 ⎤4/27⎥ ⎢ ⎥⎥ ⎢− 3.6 .⎥25/27⎥⎦⎢⎣1.8 ⎥⎦The solution of this equation isc = , c = −4, c 2 .0212=Substituting these values in equation (2) we obtainy ( x)= 2L0 ( x)− 4L2( x)+ 2L3( x)ory ( x)= x2which is the exact solution.Example3. Let us now take the equation11 7 6 3 2 2557 11322y ( x)= x + 2x− x + 5x+ 44x− x + + ∫ 7( x + xt + t ) y(t)dt .117 9−1.Next, we substitute these matrices in equation (11) and then simplify to obtainIf we use expression (10) for i , j = 0,1, 2 we obtain the fixed matrixFollowing the previous procedures, we get the exact solution of linear Fredholm integral equation forN = 11 as11 7 6 3y ( x)= x + 2x− x + 5x+ x − 3which is the exact solution.Example 4. We consider the problem13x1 3y( x)= e − (2e+ 1) x + ∫ xty(t)dt .90We give numerical analysis for N = 8, 10 in Table 1 and Figure 1.1