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Hence theorems in [34, 35] cannot be applied to solve this example.

end{aligned} We solve this example using the proposed method with several values of (tau, N), and α.

We use CG to solve this example and the optimal lifetime (i.e., 50) has been found in 2 iterations.

To illustrate the superiority of Algorithm 1, we also implement the inexact ADMM (denoted by IADMM) presented in [25] to solve this example under the same computational environment.

Example 2 In order to illustrate the reliability and efficiency of the a posteriori error estimates in Theorem 4.1, we use Algorithm 5.3 to solve this example.

Note that we cannot solve this example using a global method because the number of reachable states is infinite.

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Again, we solved this example by this method and the results are given in Table 5.

They solved this example by finite difference and finite element methods.

Therefore, in addition to the existing solution, a genetic algorithm has been used to solve this model in the numerical example section.

Although many solutions are adopted to solve this problem, for example shielding, filtering and grounding, noise is still introduced into the circuit inevitably.

In this paper we present our approach to solve this issue and examples that show its correctness.

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