Numerical study of the boundary layer problem over a flat plate by orthogonal cubic spline basis functions

In this paper, the laminar boundary layer flow over a flat plate, governed by the Prandtl equations, has been studied numerically. The problem is a dimensionless third-order system of nonlinear ordinary differential equations which arises in boundary layer flow. This system is solved using an orthogonal basis for the space of cubic splines (O-splines), as an approximation tool. Some new properties of O-splines have been explored. Also, more accurate values for the initial value of the second derivative of the Falkner–Skan equation are obtained as an initial value inverse problem. Using the new initial values, the problem becomes a first-order system of ordinary differential equations which is solved by the RK45 method and the results are compared with the presented method.

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