MODIFIED ALGORITHMS FOR NONCONFORMING TAYLOR DISCRETIZATION

Algorithms for solving partial differential equations which extend pre vious applications of the nonconforming Taylor discretization method ( NTDM) are presented. In one modification the number of interrelated gr id points is variable, thus enabling additional geometric flexibility. Another modification is the approximation of the governing differenti al equation using the method of weighted residuals. A simple one-dimen sional test case with a known analytic solution is solved using this c ode. The results demonstrate that precision is enhanced when using the method of weighted residuals with an increased number of interrelated points. The algorithm is applied as a general purpose two-dimensional code for nonlinear steady state heat-conduction. Two-dimensional exam ples with complex geometry and boundary conditions are then solved bot h by the NTDM and by the finite elements method (FEM). The results obt ained by the two methods are compared.