The development of an electronic circuit simulation system using variable tabular bases

The object of the study is a system for electronic circuit simulation using variable tabular bases, which optimizes the calculation processes in complex circuits. The work addressed the problem of creating models of electronic circuits with a convenient description of components in a linear system of equations. A method for electronic circuit simulation using variable tabular bases is presented. The problem addressed is improving the efficiency of simulation of electronic circuits of varying complexity through the use of two approaches: the General Tabular Model (GTM) and the Hybrid Model 10 (HM10). The results obtained demonstrate that the GTM provides a universal approach to modeling due to the rapid formulation of equations but leads to an increase in the matrix dimensions. In contrast, the HM10 significantly reduces the number of variables in the equations, although it requires additional computations to achieve complete results. The system architecture includes the ability to change the tabular basis or create a custom tabular basis to adapt to specific electronic circuit modeling tasks, thanks to the efficient use of Python libraries such as NumPy. The features and distinctive characteristics of the proposed system are the variability of tabular bases for optimal problem-solving, as well as the modularity of the system, which ensures its flexibility and scalability. Additionally, the system allows adding new components and adapting algorithms to specific scenarios. The practical application of the results covers educational processes, scientific research, as well as automated analysis and optimization of the design of complex electronic devices. The system is effective for working with complex circuits containing nonlinear components and provides fast solutions to algebraic equations. The obtained results showed that for a certain circuit configuration, the size of the model matrix can be 1.5 to 2 times smaller, which significantly reduces the number of calculations