The work to be presented concerns numerical solution of nonlinear two-point boundary value problems. We show that the quasi-linearization method (Newton method on operator level) can be used as a basis to derive (i) the FDM with Newton method and (ii) the shooting by Newton method. The same relation holds for the Picard and the constant-slope methods. Based on these results, we propose (i) a replacement of the FDMs for nonlinear problems (the relaxation methods) by respective successive application of the linear shooting method and (ii) a shooting by Picard method (shooting-projection method). We discuss the advantages of the proposed approaches and present examples.
Successive application of the linear shooting method for numerical solution of nonlinear two-point boundary value problems
2018. 10. 18. 10:15
BME H. épület 306-os terem
Stefan Filipov (Department of Computer Science, Faculty of Chemical System Engineering, University of Chemical Technology and Metallurgy, Sofia, Bulgaria)