Generalized Gearʹs method for computing the flow of a viscoelastic fluid Original Research Article

A fourth-order predictor-corrector method is developed for obtaining the numerical solution of a class of singular boundary value problems in which the highest derivative is further multiplied by a parameter which can take arbitrarily small values. First, the method is tested on a prototype linear differential equation. It is then used to compute the two-dimensional stagnation point flow of a viscoelastic fluid. Finally, the flow over a stretching sheet is computed for which an exact solution exists. The comparison of the results shows that the method gives highly accurate results for a moderately sized integration step.