A GALERKIN SOLUTION TO A REGULARIZED CAUCHY SINGULAR INTEGRODIFFERENTIAL EQUATION

This paper presents a Galerkin approach for solving a regularized vers ion of the Cauchy singular, linear integro-differential equation d The ta/dx(x) - f(x) = lambda integral(y=0)(1) Theta(y)/x-y dy, x is an ele ment of (0, 1), subject to Theta(0) = Theta(1) = 0. This equation has appeared in both combined infrared gaseous radiation and molecular con duction, and elastic contact studies. A regularized formulation is pro duced which suggests the use of an expansion technique where the ortho gonal basis functions are chosen as the Chebychev polynomials of the f irst kind. Accurate results, requiring a minimal computational cost, a re formally documented and compared to a purely numerical solution.