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A BVP solver that controls residual and error. (English) Zbl 1154.65063

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.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations

Software:

bvp4c; Matlab; COLSYS
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