Abstract
For the Falkner–Skan boundary layer equation we develop an innovative method by transforming the third-order governing equation into a non-linear system of three first-order ordinary differential equations (ODEs), whose coefficient matrix is zero trace. Hence, we can solve it by using an SL(3,R) Lie-group shooting method, which allows us to search a missing initial value A at the left-end; moreover, A can be expressed as a closed-form function of r∈[0,1], where the best r is determined iteratively by matching the right-end boundary conditions. The present method converges very fast. When the target equation is matched precisely, the initial value A can be obtained accurately, and then we can apply the fourth-order Runge–Kutta (RK4) method to obtain a rather accurate numerical solution.
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