International Journal on Science and Technology

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Numerical Simulation of Indoor Carbon Dioxide Concentration in a Small Classroom Using the Fourth-Order Runge–Kutta Method

Author(s) Mrs. Kejia Jandu, Dr. Vinod Kumar Sharma
Country India
Abstract Indoor air quality is an important real-life issue in classrooms, offices, tuition centres, libraries, and small meeting rooms. Carbon dioxide concentration increases when people remain in a closed room and decreases when ventilation improves. This paper presents a simple numerical model for estimating indoor carbon dioxide concentration in a small classroom using the fourth-order Runge–Kutta method. The study combines applied mathematics, environmental science, education, and building management. A first-order ordinary differential equation was developed to describe the balance between carbon dioxide generation and ventilation removal:

dC/dt=p-k(C-C_o),

where C(t) is indoor carbon dioxide concentration in parts per million, C_o is outdoor carbon dioxide concentration, p is the indoor generation rate, and k is the ventilation removal coefficient. A classroom scenario was considered with C_o=420 ppm, initial indoor concentration C(0)=430 ppm, generation rate p=16 ppm/min during class, and ventilation coefficient k=0.050 〖"min" 〗^(-1). After 60 minutes, the occupants were assumed to leave and improved ventilation was applied with p=0 and k=0.080 〖"min" 〗^(-1). The fourth-order Runge–Kutta method was applied using a step size of 5 minutes over a 120-minute period. The numerical results were compared with the exact solution for validation. The model predicted that indoor concentration increased to 724.564 ppm after 60 minutes and decreased to 422.510 ppm after 120 minutes. The maximum numerical error was only 0.032 ppm. The results show that the differential equation solved by a standard numerical method can support practical understanding of indoor air quality.
Keywords Runge–Kutta Method, Numerical Method, Differential Equation, Indoor Air Quality, Carbon Dioxide, Classroom Ventilation, Real-Life Problem, Initial Value Problem
Field Mathematics
Published In Volume 17, Issue 3, July-September 2026
Published On 2026-07-15
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Crossref DOI prefix of IJSAT is 10.71097/IJSAT

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