Steady‐state analysis of nonlinear oscillatory circuits by iterative decomposition method

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<jats:title>Abstract</jats:title><jats:p>Newton's method is well known for finding the fixed point of the Poincaré mapping for steady‐state analysis of nonlinear oscillatory circuits. However, in practice, quadratic convergence of this method is not ensured due to the discretization error of the numrical integration and the errors of the approximate solutions for nonlinear equations which are solved at each time‐step of the numerical integration. This paper proposes a new method for the steady‐state analysis of nonlinear nonautonomous and autonomous systems which takes account of the numerical integration error stated above. In this method, the system of equations which includes a Poincaré mapping is discretized and reexpressed is a system of finite difference equations to which an iterative decomposition method is applied. Although this approach is essentially equivalent to the conventional Newton method based on the Poincaré mapping, it has the advantages that the Jacobian matrix can always be computed exactly for an arbitrary time‐steplength and that the local quadratic convergence of the algorithm is guaranteed. Considering these advantages, this paper also proposes a strategy to improve the computational efficiency of the algorithm in which initially, a large time step is used to find a rough solution which is then used as the starting value in the subsequent Newton iteration. Numerical examples are given to verify the relevant theorems and to show the effectiveness of the proposed algorithm.</jats:p>

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