TY - EJOU AU - Chang, Chih-Wen AU - Liu, Chein-Shan TI - A New Optimal Iterative Algorithm for Solving Nonlinear Poisson Problems in Heat Diffusion T2 - Computers, Materials \& Continua PY - 2013 VL - 34 IS - 2 SN - 1546-2226 AB - 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 αc 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. KW - Nonlinear algebraic equations KW - Nonlinear Poisson equation KW - Iterative algorithm KW - Modified globally optimal iterative algorithm (MGOIA) Invariant manifold DO - 10.3970/cmc.2013.034.143