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On finite difference approximation of a matrix-vector product in the Jacobian-free Newton-Krylov method. (English) Zbl 1258.65049
The authors present methods for approximating the Jacobian-vector product for the Jacobian-free Newton-Krylov method including finite difference schemes, which are forward, backward and central finite difference schemes, and the finite difference step size. The error of these schemes is analyzed and the theoretical basis for choosing the finite difference step size is presented. Finally, the applicability of the proposed method is illustrated by solving a radiation diffusion problem and the Bratu problem. Numerical results demonstrate the effectiveness of the finite difference methods.

65H10 Numerical computation of solutions to systems of equations
65N06 Finite difference methods for boundary value problems involving PDEs
35J60 Nonlinear elliptic equations
Full Text: DOI
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