Solusi Numerik Radial Basis Function dan Runge Kutta pada model perubahan suhu dinding rumah

Abstract

Citizenship Education in higher education plays a crucial role in shaping students into critical thinkers, This study presents a numerical investigation of a heat-transfer model describing temperature variation on a house wall based on Newton’s law of cooling, where the heat transfer coefficient is assumed to vary over time. The governing first-order differential equation is solved using two different numerical approaches: the Radial Basis Function (RBF) method and the fourth-order Runge–Kutta (RK4) method. The RBF method is implemented as a meshless interpolation technique to construct a smooth approximate solution, while the RK4 method is employed as an explicit stepwise numerical solver with a fixed time increment. Simulation results show that the RBF method produces a smooth solution that closely interpolates the data points, although it is computationally demanding and highly dependent on parameter selection. In contrast, the RK4 method provides a stable and computationally efficient solution, but its accuracy is influenced by the chosen step size. Overall, both methods successfully approximate the temperature evolution described by the model, yet each demonstrates different strengths depending on computational and application requirements.