Generalized Quasilinearization Methodand Higher Order of Convergence for Second-order Boundary Value Problems
نویسندگان
چکیده
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 show the application of the generalized quasilinearization method developed here for second-order boundary value problems.
منابع مشابه
The Method of Generalized Quasilinearization and Higher Order of Convergence for Second-Order Boundary Value Problems
The generalized quasilinearization method for second-order boundary value problem has been extended when the forcing function is the sum of two functions without require that any of the two functions involved to be 2-hyperconvex or 2-hyperconcave. Two sequences are developed under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergen...
متن کاملGeneralized Quasilinearization for Nonlinear Three-point Boundary Value Problems with Nonlocal Conditions
We apply the generalized quasilinearization technique to obtain a monotone sequence of iterates converging quadratically to the unique solution of a general second order nonlinear differential equation with nonlinear nonlocal mixed three-point boundary conditions. The convergence of order n (n ≥ 2) of the sequence of iterates has also been established.
متن کاملGeneralized quasilinearization method for a second order three point boundary-value problem with nonlinear boundary conditions
The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order differential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.
متن کاملTENSION TRIGONOMETRIC SPLINES INTERPOLATION METHOD FOR SOLVING A LINEAR BOUNDARY VALUE PROBLEM
By using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2VBP) withDirichlet, Neumann and Cauchy types boundary conditions. The moment at the knots isapproximated by central finite-difference method. The order of convergence of the methodand the theory is illustrated by solving tes...
متن کاملA Higher Order Monotone Iterative Scheme for Nonlinear Neumann Boundary Value Problems
The generalized quasilinearization technique has been employed to obtain a sequence of approximate solutions converging monotonically and rapidly to a solution of the nonlinear Neumann boundary value problem.
متن کامل