Rational function approximations in the numerical solution of Cauchy-type singular integral equations

Michael A. Driscoll, R.P. Srivastav
1985 Computers and Mathematics with Applications  
Cauchy-type singular integral equations of the second kmd with constant coefficients are solved via rational and polynomial approximations. Rational functions. similar to that of polynomials. have the property that for r(f) rational and for many of the weight functions MI(!) encountered in practice, is also rational. Hence. approximations by rational functions IS feasible. Rational function approximations in the solution of the dommant equation results in a linear algebraic system which
more » ... s blockdiagonal structure. It is further shown that the determinant of the coefficient matrix is bounded below away from zero and stability is ensured under fairly non-restrictive conditions. For the complete Cauchytype singular integral equation. i.e. the equation with both the principal and regular parts, gaussian quadrature in conjunction with the rational function method is synthesized in the construction of a "hybrid" scheme. Error estimates and convergence are established. A variety of problems from Aerodynamics and FraCtUre Mechamcs are solved and presented as a basis of comparison to polynomialbased schemes.
doi:10.1016/0898-1221(85)90099-9 fatcat:x43ayy3r7vapjg6qon6pq6z4iy