Several engineering applications need a robust method to find all the roots of a set of nonlinear equations automatically. The proposed method guarantees monotonous convergence, and it can determine whole submanifolds of the roots if the number of unknowns is larger than the number of equations. The critical steps of the multidimensional bisection method are described and possible solutions are proposed. An efficient computational scheme is introduced. The efficiency of the method is characterized by the box-counting fractal dimension of the evaluated points. The multidimensional bisection method is much more efficient than the brute force method. The proposed method can also be used to determine the fractal dimension of the submanifold of the solutions with satisfactory accuracy. KeywordsBisection method · multi dimension · system of non-linear equations · multiple roots · efficiency number Acknowledgement This work is connected to the scientific program of the "Development of quality-oriented and harmonized R+D+I strategy and functional model at BME" project. This project is supported by the New Széchenyi Plan (

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SummaryAn efficient numerical method is presented to analyze the moment stability and stationary behavior of linear stochastic delay differential equations. The method is based on a special kind of discretization technique with respect to the past effects. The resulting approximate system is a high dimensional linear discrete stochastic mapping. The convergence properties of the method is demonstrated with the help of the stochastic Hayes equation and the stochastic delayed oscillator.

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