A Spectral Quasilinearization Parametric Method for Nonlinear Two-Point Boundary Value Problems
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In this paper, we develop an efficient explicit method based on the spectral parametric iteration method and quasilinearization scheme, which can be used for the efficient numerical solution of nonlinear stiff/nonstiff two-point boundary value problems. The method derived here has the advantage that it does not require the solution of nonlinear systems of equations. We derive the method, which requires one evaluation of the Jacobian and one LU decomposition per step. Some numerical experiments on nonlinear stiff/nonstiff problems show the efficiency and accuracy of the method. Moreover, the method provides us a simple way to control and modify the convergence rate of the solution.
KeywordsSpectral parametric iteration method Quasilinearization method Two-point boundary value problems Nonlinear boundary conditions Van Der Pol equation
Mathematics Subject Classification34B15 41A10
This research was supported by a grant from Ferdowsi University of Mashhad (No. 2/42583). Further, the authors are very grateful to the editor and referees for their comments and suggestions.
- 9.Kincaid, D.R., Cheny, E.W.: Numerical Analysis Mathematics of Scientific Computing. Brooke Cole, California (2001)Google Scholar
- 15.Saberi-Nadjafi, J., Ghorbani, A.: Piecewise-truncated parametric iteration method: a promising analytical method for solving Abel differential equations. Z Naturforsch. 65a, 529–539 (2010)Google Scholar