Abstract:
A method for solving the integral equations by(x)=f(x)+ f K(x,t) y(t) dta is introduced. The kernel K(x,t) is approximated in the variable x univariately, leaving t dependence unchanged. The degenerate kernel approximation is defined to K(x,t) by n K(x,t) ai(x) K (xi,t) i=1 and then the problem is the choice of the above approximation, in particular, we consider the use of piecewise linear and piecewise Hermite interpolation theory over a sub-division of the domain of x. This gives explicit representations for the functions ai (x) and allows the use of quadrature on each sub-interval. The theory of piecewise linear and piecewise cubic Hermite interpolation is illustrated.
Page(s):
77-86
DOI:
DOI not available
Published:
Journal: Research journal, Volume: 1, Issue: 2, Year: 1987