The code is for the manuscript:
Yet another code for Boundary Value Problems- Higher Derivative Method
Jerry Chen, Dayaram Sonawane, Kishalay Mitra, and Venkat R. Subramanian
While there are many good existing solvers, in this paper, a discretization scheme using higher derivative method (HDM) with A-stability property is implemented for the efficient solution of boundary value problems (BVPs) described by Ordinary Differential Equations (ODEs). The proposed approach uses nth derivative to get 2n order of accuracy at each node point in BVPs. The derivation of HDM equations can be related to the stability function of the Implicit Rung-Kutta methods (IRK) and Padé approximation, and the coefficients of the HDM equations can be found by Hermite collocation methods. Once the analytical derivatives are found, it is applied for every node in HDM equations. The illustrative examples are included to demonstrate the applicability of HDM for the solution of BVPs. The algorithm is successfully implemented, demonstrated and shared as an open access Maple® code.
The Manuscript can be downloaded here [pdf].
1. Troesch’s problem [mws][pdf]
2. Unknown parameter problem [mws][pdf]
3. For parameter estimation and optimal control [mws][pdf]
- Please put the code and the *.mws file under the same directory or redirect the code to “HDM.txt” file.
- *.mws file is executable by Maple (Maplesoft)
- Right click on the link and choose "save link as ..." to download the Maple codes
All the 35 test problems provided on Cash’s website were tested by the proposed HDM approach. The problem set can be found on Jeff Cash’s website: http://wwwf.imperial.ac.uk/~jcash/BVP_software/PROBLEMS.PDF
Cash’s 35 test problems with stiff parameters by HDM method [mws] [pdf]
Please feel free to contact Dr. Venkat Subramanian for any comments.