MATHEMATICAL MODELING AND ANALYSIS OF TEMPERATURE CONTROL PROCESSES IN SMART HOME SYSTEMS

Authors

  • Ulug'bek Suyarov Farg'ona davlat universiteti Author
  • Shuxratjon Axmadaliyev Fergana State University Applied Mathematics Department 3rd year student Author https://orcid.org/0009-0009-2478-5571
  • Sobirjonov Siyovushxo‘ja Fergana State University Applied Mathematics Department 3rd year student Author

Abstract

This paper examines the problem of real-time mathematical modeling of indoor temperature distribution in smart home systems. The study is based on the heat diffusion equation  from mathematical physics, implemented via HTML5, CSS3, and JavaScript on a 30×50 discrete grid using the Explicit Euler numerical method. Physical realism is ensured by radiator, window, and door boundary conditions, stochastic noise effects, and a multi-stage color gradient visualization.

Author Biographies

  • Shuxratjon Axmadaliyev, Fergana State University Applied Mathematics Department 3rd year student

    Fergana State University Applied Mathematics Department 3rd year student

  • Sobirjonov Siyovushxo‘ja , Fergana State University Applied Mathematics Department 3rd year student

    Sobirjonov Siyovushxo‘ja Fergana State

    University Applied Mathematics Department

    3rd year student

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Published

2026-09-29

Issue

Vol. 1 No. 8 (2026): SCIENTIFIC RESEARCH, INNOVATIONS, AND MODERN APPROACHES

Section

Articles