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<p>One key factor in maintaining a stable economy is controlling business cycles, which are influenced by investment decisions based on past economic conditions. This can be addressed through appropriate macroeconomic policies. In this study, we numerically simulate an enhanced Kalecki model that incorporates investment-related delays and plays a crucial role in analyzing business cycles described by an integro-differential equation with a special nonlinear term. The simulation is carried out using the meshless discrete Galerkin method, which operates on irregular nodes via the moving least squares (MLS) approach. The MLS approximation provides a local polynomial fitting framework using weight functions, which reduces computational complexity and enhances numerical stability. Moreover, the inherent stabilization strategy of the MLS method mitigates sensitivity to the distance between nodes, a beneficial feature retained in the proposed approach. The method presents a straightforward and versatile algorithm, readily implementable on a standard personal computer and adaptable to other delay integro-differential equations arising in diverse areas of applied science. To assess the method’s reliability, we perform an error analysis, determine the convergence order, and apply the method to several numerical examples. The results demonstrate its effectiveness and validate the analytical predictions.</p>

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A numerical approach to simulate the delay Kalecki model describing business cycles using MLS-Galerkin method

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Yadollah Ordokhani,
  • Alireza Hosseinian,
  • Pouria Assari

摘要

One key factor in maintaining a stable economy is controlling business cycles, which are influenced by investment decisions based on past economic conditions. This can be addressed through appropriate macroeconomic policies. In this study, we numerically simulate an enhanced Kalecki model that incorporates investment-related delays and plays a crucial role in analyzing business cycles described by an integro-differential equation with a special nonlinear term. The simulation is carried out using the meshless discrete Galerkin method, which operates on irregular nodes via the moving least squares (MLS) approach. The MLS approximation provides a local polynomial fitting framework using weight functions, which reduces computational complexity and enhances numerical stability. Moreover, the inherent stabilization strategy of the MLS method mitigates sensitivity to the distance between nodes, a beneficial feature retained in the proposed approach. The method presents a straightforward and versatile algorithm, readily implementable on a standard personal computer and adaptable to other delay integro-differential equations arising in diverse areas of applied science. To assess the method’s reliability, we perform an error analysis, determine the convergence order, and apply the method to several numerical examples. The results demonstrate its effectiveness and validate the analytical predictions.