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On the Chaplygin method for the Darboux problem

100%
Jaruszewska-Walczak D.
Commentationes Mathematicae
|
2007
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tom 47
|
nr 1
EN
In the paper we deal with the Darboux problem for hyperbolic functional differential equations. We give the sufficient conditions for the existence of the sequence \(\{z^{(m)}\}\) such that if \(\tilde{z}\) is a classical solution of the original problem then \(\{z^{(m)}\}\) is uniformly convergent to z\(\tilde{z}\). The convergence that we get is of the Newton type.
2
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A Newton-Kantorovich-SOR type theorem

88%
Finta B.
Open Mathematics
|
2005
|
tom 3
|
nr 2
282-293
EN
In this paper we propose a new method for solving nonlinear systems of equations in finite dimensional spaces, combining the Newton-Raphson's method with the SOR idea. For the proof we adapt Kantorovich's demonstration given for the Newton-Raphson's method. As applications we reobtain the classical Newton-Raphson's method and the author's Newton-Kantorovich-Seidel type result.
3
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An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

63%
Barboteu M., Bartosz K., Kalita P.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
|
nr 2
263-276
EN
We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.
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