Some experiments with high order compact methods using a computer algebra software—Part I

We consider a procedure for obtaining a compact fourth order method to the steady 2D Navier–Stokes equations in the streamfunction formulation using the computer algebra system Maple. The resulting code is short and from it we obtain the Fortran program for the method. To test the procedure we have solved many cavity-type problems which include one with an analytical solution and the results are compared with results obtained by second order central differences to moderate Reynolds numbers.