A new optimal iterative algorithm for solving nonlinear poisson problems in heat diffusion

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作者：
机构：
[1] Chang, Chih-Wen
[2] Liu, Chein-Shan
来源：
Chang, C.-W. (0903040@nchc.narl.org.tw) | 2013年 / Tech Science Press卷 / 34期
关键词：
Convergence rates - Convergence speed - Invariant manifolds - Iterative algorithm - Nonlinear algebraic equations - Nonlinear Poisson equations - Numerical experiments - Solution vectors;
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摘要：
The nonlinear Poisson problems in heat diffusion governed by elliptic type partial differential equations are solved by a modified globally optimal iterative algorithm (MGOIA). The MGOIA is a purely iterative method for searching the solution vector x without using the invert of the Jacobian matrix D. Moreover, we reveal the weighting parameter ac in the best descent vector w = αcE + DTE and derive the convergence rate and find a criterion of the parameter γ. When utilizing αc and γ, we can further accelerate the convergence speed several times. Several numerical experiments are carefully discussed and validated the proposed method. © 2013 Tech Science Press.
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