Geodesic
The method of continuous continuation by a parameter for solving boundary-value problems for nonlinear systems of differential-algebraic equations with delay that have singular points
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 38-45

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In this paper, we consider a numerical method for solving a nonlinear boundary-value problem for a system of differential-algebraic equations with a delayed argument that have singular limit points. For a numerical solution of the boundary-value problem, the shooting method is used. The value of the shooting parameter is calculated by the Newton method. We consider the case where the problem is ill-posed and hence the method may diverge. In this case, the solution is constructed by the method of the best parameter, namely, the length of the curve of the set of solutions. The solution of the initial problem for each value of the shooting parameter is calculated using the method of continuous continuation by the best parameter.
Keywords: numerical method, boundary-value problem, differential equation with delay, shooting method, method of continuation by the best parameter, singularly perturbed equation. 
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     author = {M. N. Afanaseva and E. B. Kuznetsov},
     title = {The method of continuous continuation by a parameter for solving boundary-value problems for nonlinear systems of differential-algebraic equations with delay that have singular points},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {38--45},
     publisher = {mathdoc},
     volume = {192},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_192_a3/}
}
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M. N. Afanaseva; E. B. Kuznetsov. The method of continuous continuation by a parameter for solving boundary-value problems for nonlinear systems of differential-algebraic equations with delay that have singular points. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 38-45. http://geodesic.mathdoc.fr/item/INTO_2021_192_a3/