AN ALTERNATING DIRECTION IMPLICIT METHOD FOR ORTHOGONAL SPLINE COLLOCATION LINEAR-SYSTEMS

An Alternating Direction Implicit method is analyzed for the solution of linear systems arising in high-order, tensor-product orthogonal spline collocation applied to some separable, second order, linear, elliptic partial differential equations in rectangles. On an N x N partition, with Jordan's selection of the acceleration parameters, the method requires O(N2 ln2 N) arithmetic operations to produce an approximation whose accuracy, in the H-1-norm, is that of the collocation solution.