Question: Numerical analysis AFredholmintegralequationofthesecondkindisanequationoftheform u ( x ) = f ( x ) + a b K ( x , t ) u ( t )

Numerical analysis

AFredholmintegralequationofthesecondkindisanequationoftheform

u(x)=f(x)+abK(x,t)u(t)dtx[a,b]

whereaandbandthefunctions f andK aregiven.Toapproximatethefunctionu ontheinterval[a,b] ,apartitiona=x0<x1<<xm=bisselectedandtheequations

u(xi)=f(xi)+abK(xi,t)u(t)dti=0,1,...,m

aresolvedforu(x0),u(x1),...,u(xm).Forthisproblem,considera=0,b=1,f(x)=3x2+42exe1x,andK(x,t)=ext .

Showthatu(x)=x2 isthesolutiontotheintegralequationin[0,1]

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