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All versions of SPICE can perform various kinds of analysis such as operating point, sensitivity, and transient analyses, and many others. The algorithms used for computations are based on an iterative numerical solution of nonlinear differential equations. This paper gives a simple overview about these algorithms, their principles, function and disadvantages. It introduces a novel approach and implementation of implicit and explicit algorithms for solving the differential equations in circuit design with the aim to improve the reliability and efficiency of the solution. Furthermore, it presents a comparison between the standard SPICE algorithm and the new developed ones.