We will combine linear successive overrelaxation method with nonlinearmonotone iterative scheme to obtain a new iterative method for solving nonlinear equations. Thebasic idea of this method joining traditional monotone iterative method (known as the methodof lower and upper solutions) which depends essentially on the monotone parameter is that byintroducing an acceleration parameter one can construct a sequence to accelerate the convergence. The resulting increase in the speed of convergence is very dramatic. Moreover, the sequence canaccomplish monotonic convergence behavior in the iterative process when some suitable accelerationparameters are chosen. Under some suitable assumptions in aspect of the nonlinear function andthe matrix norm generated from this method, we can prove the boundedness and convergence ofthe resulting sequences. Application of the iterative scheme is given to a logistic model problemin ecology, and numerical results for a test problem with known analytical solution are given todemonstrate the accuracy and efficiency of the present method.
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