Stepping forward from a previous conference contribution, the article focuses on extension of inverse problem algorithms to integral-differential modelling and formal/strict demonstration of graphical-optimization method. It shows evident-mathematical and 3D-imaging proofs of the graphical optimization method with L1 Norm simulations and algorithms. At present, Linear/Nonlinear Optimization mathematical methods constitute the choice of preference in getting improvements for erosion and corrosion simulations- determinations in general tribology, biotribology and tribocorrosion. The method(s) developed are classical numerical optimization settings for objective functions, programming optimization and simulations, and special software for imaging in 3D. Results are diverse and the range of their applications is wide. First, the article provides a definite formal demonstration of the nonlinear graphical optimization both in numerical results and in imaging. Then, the authors propose the development of programming optimization and mathematical proofs-algorithms of the integral-differential model for various models. Subsequently, an overview of stochastic erosion methods based on Markov Chain is presented in the article. Finally, the second generation of tribology models is defined and conceptually explained. To summarise, the article comprises new findings towards modernization of tribology, biotribology and tribocorrosion models, gathering innovative research branches for future extension of the mathematical modelling progress. The results can be applied to both general techniques and mechanical engineering. The analytical and numerical demonstration of the integral-differential model constitutes a key point and essential result of the research. Extension to electromagnetic and electronic models of these methods is also considered feasible and practical
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