The method of Quasilinearization which was developed by Bellman and Kalaba covers the situation when the forcing function is either convex or concave. Here, we describe the process of the Quasilinearization method being extended, refined and generalized so as to include forcing functions which are the sum of a convex and concave function. This includes many special cases which are extensions of...

We apply a method of quasilinearization to a boundary value problem for an ordinary differential equation on an unbounded domain. A uniquely determined Green’s function, which is integrable and of fixed sign, is employed. The hypotheses to apply the quasilinearization method imply uniqueness of solutions. The quasilinearization method generates a bilateral iteration scheme in which the iterates...

We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid a...

The method of generalized quasilinearization for second-order boundary value problems has been extended when the forcing function is the sum of 2-hyperconvex and 2-hyperconcave functions. We develop two sequences under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergence is of order 3. Finally, we provide numerical examples to sho...

Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. While the WKB method generates an expansion in powers of h̄, the quasilinearization method (QLM) approaches the solution of the nonlinear equation obtained by casting the Schrödinger equation into the Riccati form by approximating nonlinear terms by a sequence of linear ones. It does not rely on the ex...