On accelerated monotone iterations for numerical solutions of semilinear elliptic boundary value problems |
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Institution: | Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China;Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai 200234, People’s Republic of China |
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Abstract: | This paper is concerned with the computational algorithms for finite difference solutions of a class of semilinear elliptic boundary value problems. An accelerated monotone iterative scheme is presented by using the method of upper and lower solutions. The rate of convergence of the iterations is estimated by the infinity norm, and the rate of convergence is quadratic for a larger class of nonlinear functions, including monotone nonincreasing functions. An application is given to a logistic model problem in ecology. |
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