Numerical study of the boundary layer problem over a flat plate by orthogonal cubic spline basis functions
Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, 41938, Rasht, Iran
2 Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, P.O. Box 1914, 41938, Rasht, Iran
Accepted: 22 July 2021
Published online: 28 July 2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021