An iterative method based-on eigenfunctions and adjoint eigenfunctions for solving the Falkner-Skan equation

For the Falkner-Skan boundary layer equation we develop a new iterative method by transforming it into an integral equation, which is solved by using the eigenfunctions as test functions, and at the meantime, the adjoint eigenfunctions are used to be the bases to expand the numerical solution. Due to the bi-orthogonality of eigenfunctions and adjoint eigenfunctions we can find the expansion coefficients of numerical solution in closed-form. Hence, the iterative scheme converges very fast to find the multiple solutions of Falkner-Skan equation.