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A deferred correction method for nonlinear two-point boundary value problems: Implementation and numerical evaluation. (English) Zbl 0727.65070

For first order nonlinear two-point boundary value problems \((*)\quad dy/dx=f(x,y),\) \(a\leq x\leq b,\) \(g(y(a),y(b))=0\) the authors describe the implementation of a method which combines the ideas of collocation and deferred correction using mono-implicit Runge-Kutta schemes. To optimize the stepsize in view of error estimations and to ensure the convergence of Newton iterations strategies for adding and removing grid points are explained.
The implemented algorithm (the code is called HAGRON) has been successfully tested for 13 singularly perturbed problems known from other publications. The numerical tests are abundantly discussed in comparison with the codes COLSYS and COLNEW. The authors point out that HAGRON is a useful tool for solving problems of type (*).

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations

Software:

COLNEW; COLSYS
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