Accurate Chebfun solutions to third-order nonlinear BVPs on the half-line. Applications in boundary layer theory

Abstract The paper is devoted to obtaining accurate numerical solutions to some third-order nonlinear boundary problems on the real semi-axis of Blasius type. It aims to address these issues more accurately as boundary value problems rather than converting them into initial value problems. The Blasius boundary layer problem with slip and nonslip boundary conditions, the Sakiadis and Falkner-Skan problems, a pseudoplastic boundary layer problem, etc, are solved using the Chebyshev technology, in the form of Chebfun, along with the domain truncation. The choice of this method is justified vis-à-vis the difficulties of solving some singular and nonlinear third-order boundary value problems. The convergence rate and the convergence order of Newton’s method in solving the nonlinear algebraic system obtained by discretisation are established. The shear stress is accurately estimated along with the first and second derivatives of the solutions. Some comments on the stability of numerical outcomes concerning the length of the integration domain are provided. The results are presented graphically and tabulated for the most challenging case (non-linearity involving fractional power). The method correctly captures the large gradients of the solution.