A novel collocation-based numerical method for higher-order linear ODE systems with pharmacokinetic applications

This paper introduces a collocation method founded on the independence polynomial of the path graph to solve systems of linear differential equations subject to mixed conditions. The approach converts the original differential system and its associated conditions into an equivalent matrix representation, resulting in a linear algebraic system whose unknowns are the independence coefficients. Several test problems are conducted to assess the numerical efficiency and accuracy of the method. As a practical application, the technique is applied to the three-compartment pharmacokinetic model, illustrating its robustness, numerical stability, and computational simplicity. The results demonstrate the proposed method’s effectiveness and reliability in solving complex systems of differential equations.

کلیدواژه ها:

Systems of differential equations ، graph ، Independence polynomial ، Collocation method ، compartment pharmacokinetic model