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...

The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schrödinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was discussed recently by one of the present authors (VBM), approaches the solution of a nonlinear differential equation by approximating the nonlinear terms by a seq...

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...

We study existence and approximation of solutions of some Neumann boundary-value problems in the presence of an upper solution β and a lower solution α in the reversed order (α ≥ β). We use the method of quasilinearization for the existence and approximation of solutions. We also discuss quadratic convergence of the sequence of approximants.

We study the existence of solutions for a periodic fourth order problem. We prove an associated uniform antimaximum principle and develop a method of upper and lower solutions in reversed order. Furthermore, by the quasilinearization method we construct an iterative sequence that converges quadratically to a solution.

The method of quasilinearization is applied to the nonlinear second order dynamic equations with m-point boundary conditions on time scales, and two sequences could be constructed which converge uniformly to the unique solution of the m-point boundary value problems from above and below with high rate of convergence. AMS Subject Classifications: 34B15, 39A12.

The influence of non-uniform slot suction (injection) into a steady, MHD boundary layer flow over a sphere with variable viscosity has been examined. The system of nonlinear, coupled partial differential equations governing the non-similar flow have been solved numerically and the solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation...

A finite element method involving collocation method with quintic B-splines as basis functions has been developed to solve tenth order boundary value problems. The fifth order, sixth order, seventh order, eighth order, ninth order and tenth order derivatives for the dependent variable are approximated by the central differences of fourth order derivatives. The basis functions are redefined into...