Approximation of the solution of certain nonlinear ODEs with linear complexity |
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Authors: | Ezequiel Dratman |
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Affiliation: | Instituto de Ciencias, Universidad Nacional de General Sarmiento, Juan M. Gutiérrez 1150 (B1613GSX) Los Polvorines, Buenos Aires, Argentina |
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Abstract: | We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the “continuous” equation. Furthermore, we exhibit an algorithm computing an ε-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required. |
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Keywords: | 65H10 65L10 65L12 65H20 65Y20 |
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