Mechanistic tumor-response models that are transparent and updatable with patient data are important for model-informed precision radiotherapy. This study presents a reproducible computational framework integrating an explicit mathematical derivation, numerical solver, clinical protocol-derived parameters, and three-dimensional visualization to simulate simplified lung tumor regression during radiotherapy for non-small cell lung cancer (NSCLC). A first-order Taylor approximation, equivalent to the forward Euler method, is derived from Taylor's formula with integral remainder, with local truncation error of order $h^2$. The resulting update rule is applied to a first-order regression model wi... More >