A BVP Solver that Controls Residual and Error

Date of Online Publication: 31/03/2006
Keywords: Ordinary differential equations, boundary value problems, collocation, residual,
Authors: J. Kierzenka, L.F. Shampine
Pages: 27-41
We describe the algorithms and implementation of the bvp5c program for solving boundary value problems (BVPs) for ordinary differential equations. A remarkable relationship between scaled residual and true error is established for the four-point Lobatto IIIA formula. In bvp5c we exploit this relationship to obtain the robustness of a control of a scaled residual and at the same time a control of the true error that is of most interest to a user. The performance and features of the new solver are compared to those of the bvp4c solver of Matlab.


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