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Setting analog cellular computers based on cellular neural networks systems (CNNs) to change the way analog signals are processed is a revolutionary idea and a proof as well of the high importance devoted to the analog computing methods. This paper provides basics of the methods based on the CNNs paradigm that can be exploited for analog computing of very complex systems which are modelled by ODEs and/or PDEs (an implementation on chip using CNN technology is possible even an emulation in FPGA). A proof of concept of the computing approach developed in this paper is validated by solving some complex ODEs and/or PDEs models and by comparing the results obtained with those available in the literature (benchmarking). The computation based CNNs paradigm is advantageous as it provides accurate and ultra-fast solutions of very complex ODEs and PDEs.