An Efficient Newton's Method for the Numerical Solution of Fluid Integral Equations
Abstract
We propose a stable, straightforward algorithm for the numerical solution of integral equations for fluid pair distribution functions. The integral equation is not solved by Picard's standard iterative procedure but by Newton's method of solution of nonlinear equations. The large matrix appearing in Newton's method is inverted by a conjugate gradient procedure used as a rapidly converging iterative method.
 Publication:

Journal of Computational Physics
 Pub Date:
 November 1985
 DOI:
 10.1016/00219991(85)900877
 Bibcode:
 1985JCoPh..61..280Z
 Keywords:

 Fluid Dynamics;
 Integral Equations;
 Newton Methods;
 NewtonRaphson Method;
 Nonlinear Equations;
 Fourier Transformation;
 Iterative Solution;
 Fluid Mechanics and Heat Transfer