Geodesic
Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition
International Journal of Applied Mathematics and Computer Science, Tome 14 (2004) no. 1, pp. 13-18.

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Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each step.
Keywords: Newton's method, conjugate gradient method, nonlinear PDE
Mots-clés : metoda Newtona, metoda gradientu sprzężonego, warunek brzegowy nieliniowy 
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Koko, J. Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition. International Journal of Applied Mathematics and Computer Science, Tome 14 (2004) no. 1, pp. 13-18. http://geodesic.mathdoc.fr/item/IJAMCS_2004_14_1_a1/

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