An integral spline method for boundary layer equations

An integral procedure using spline polynomials is described for the two-dimensional boundary layer equations. It is a modified finite element formulation, where each term in the equations, rather than each independent variable, is approximated with a spline curve fit. For the boundary layer equations in divergence form it is shown that the spline modified finite element approach is equivalent to the class of two-point methods proposed by Keller (1975). It is shown that the Keller box scheme difference system can be reduced to an equivalent three-point system. A simpler procedure for obtaining the tridiagonal form of the Keller box scheme equations can be derived from the modified finite element method.